







Simplify 1/2^i 
20180128 

From Deepak: How do I simplify this complex equation:
z=1/(2^i) Answered by Penny Nom. 





x^2 = 16 
20161212 

From A student: x to the second power = 16
what number solves the equation? Answered by Penny Nom. 





The modulus of a complex number 
20160729 

From Cheyenne: There's a question on my Summer Assignment I cant figure out. Here it is:
Find the absolute Value of the complex number. 5i
Please help? Answered by Penny Nom. 





Complex numbers in standard form 
20160115 

From Michael: express the following complex numbers in standard form (2+3i)+(52i) Answered by Penny Nom. 





What is the value of 2((i)^(1/2))? 
20130722 

From Delilah: What is the value of 2((i)^(1/2)) ?
i.e. absolute value of 2 multiplied by square root of i. Answered by Penny Nom. 





I started with Euler's identity and manipulated it 
20111114 

From anonymous: I started with Euler's identity and manipulated it
e^i*pi=1
e^i*pi=(1)^1
e^i*pi=1
e^i*i*pi=(1)^i
e^pi=(1)^i
e^pi=(1)^i
type it in in a calculator and you get e^pi=23.1406926... and
(1)^i=0.0432139183... What did I do wrong? Answered by Robert Dawson. 





The square root of z=3+4i 
20111027 

From dianah: how to find the square roots of complex number, z=3+4i Answered by Robert Dawson. 





Find all the roots 
20101202 

From gagan: find all the roots of z^53z^4+2z^3+z^23z+2 Answered by Stephen La Rocque and Penny Nom. 





z^5  3z^4 + 2z^3 + z^2  3z + 2 
20101106 

From Kumar: would you please solve this problem, related to complex numbers.
Find all the roots of :
z^5  3z^4 + 2z^3 + z^2  3z + 2 Answered by Robert Dawson and Penny Nom. 





A Squared Number That's Negative 
20100922 

From David: What is the only number that when it's squared becomes negative? Answered by Stephen La Rocque. 





Graphical Representation of Complex Numbers 
20100608 

From Anas: why do we write complex number a+ib as (a,b)? Answered by Janice Cotcher. 





Complex roots 
20100414 

From Lan: If b and c are real numbers so that the polynomial (x^2) + bx + c has 1 + i as a zero, find b + c. Answered by Penny Nom. 





Zeros of a polynomial 
20100301 

From Gavin: Suppose the polynomial R(x) = a_9x^9+a_8x^8+...+a_1x+a_0 has real coefficients with a_9≠0. Suppose also that R(x) has the following zeros:
2,
3,
i
Using this info, answer the following.
a. What is another zero of R(x)?
b. At most how many real zeros of R(x) are there?
c. At most how many imaginary zeros of R(x) are there?
p.s. I used _ for subscript
thanks so much Answered by Harley Weston. 





A quadratic equation with roots (4i) and (4+i) 
20090505 

From Kelly: find a quadratic equation with roots (4i) and (4+i) Answered by Harley Weston. 





Find a polynomial function with the indicated zeros and satisfying the given conditions 
20090323 

From Kristen: Find a polynomial function with the indicated zeros and satisfying the given conditions. Simplofy your answer (no imaginary numbers or parentheses in the answer)
Zeros: 1+2i, 12i, 5 ; f(2)=1 Answered by Harley Weston. 





What is i^i? 
20081227 

From randomness: i have learnt that 'i' is square root of 1. What is then i^i ? It baffles my maths teacher... Answered by Robert Dawson and Penny Nom. 





Factor 9x^2 + 6x + 4 
20081121 

From Jonah: how can i solve this by factoring: 9x^2 + 6x + 4 Answered by Harley Weston. 





A quadratic equation 
20080603 

From Drew: A solution of x^28x=17 is
4 or 4+I or 4 or 4+i Answered by Janice Cotcher. 





(1i)ln(1+i) 
20080502 

From Kim: I am stuck on the expansion of (1i)ln(1+i)=(1i)[ln(square root of 2)+i(3.14/4 = 2n3.14)] Answered by Harley Weston. 





Find the quadratic equation with roots at (3i) and its complex conjugate 
20080422 

From Tiffany: Find the quadratic equation with roots at (3i) and its complex conjugate. Answered by Penny Nom. 





A complex cubic polynomial 
20080326 

From wael: how do we solve in C the following equation:
z^3 + (5i6)z^2 + (924i)z + 13i + 18 = 0 if it admits a pure imaginary root? Answered by Harley Weston. 





A complex quadratic 
20080218 

From Ash: z^2(6+2i)z+(8+6i)=0
Solve for Z Answered by Steve La Rocque and Penny Nom. 





Imaginary roots 
20071209 

From Josh: What is the correlation between imaginary roots (of a quadratic or other
polynomial equation) and the graph of the equation? As in, how can one
represent imaginary solutions graphically (and why does that work)? Answered by Harley Weston. 





Complex numbers 
20071027 

From Dylan: My problem is to prove:
z^2 = zz* Where z is the complex number x + iy and z* is it's complex conjugate x  iy.
If the absolute value of i is 1, then it looks like: z^2 = x+y x+y = x^2 + 2xy + y^2
And zz* = x^2 + y^2. for these to be equal, 2xy = 0. This seems wrong to me. What am I doing wrong? Answered by Penny Nom. 





(1  i)^5 
20070724 

From sofia: Compute the given arithmetic expression and give the answer in the form a + bi where a,b element in R.
1. (1  i)^5 Answered by Harley Weston. 





A complex number in polar form 
20070723 

From roland: write the given complex number z in polar form lzl(p+qi) where lp + qil=1 for 3  4i. Answered by Harley Weston. 





Simplifying complex denominators 
20070621 

From Krys: How do I simplify completely?
((4+i ) / (3+i ))  ((2i ) / (5i )) Answered by Stephen La Rocque. 





(1+i)^(2i) 
20070426 

From Eilis: How do I solve (1+i) to the power of 2i?
i.e. (1+i)^(2i) Answered by Penny Nom. 





12/(7  i) 
20070418 

From Diana: Perform the operation. Write all answers in a + bi form.
12

7  radical 1 Answered by Penny Nom. 





Using complex numbers 
20070312 

From Kara: Do you use complex numbers in your job? Answered by Stephen La Rocque and Penny Nom. 





Exponential form of complex numbers 
20070212 

From Austin: When dealing with imaginary numbers in engineering, I am having trouble getting things into the exponential form. The equation is 1+i now I do know that re^(theta)i = r*cos(theta) + r*i*sin(theta). Just not quite understanding the order of operations. Thanks Answered by Penny Nom. 





The absolute value of imaginary and complex numbers 
20061211 

From Keith: i don't get how to find the absolute value of imaginary and complex numbers here is an examples from the text book the answers are given but they don't show the work so i can follow along just show me the work please and explain how it is done
problem 3+4i Answered by Stephen La Rocque and Penny Nom. 





Is this unsolvable? 
20060919 

From Al: Is this unsolvable???
2xy + 3x^2  3y + y^3 = 4x + 3 where y=3. Answered by Penny Nom and Claude Tardif. 





how do i find i^22? 
20060612 

From Sky: how do i find i^{22}?
Sky Answered by Stephen La Rocque. 





sinh(i/2) 
20060209 

From Louis: How can you set up an equation to find sinh(i/2) Answered by Penny Nom. 





The square root of i 
20051130 

From Kevin:
If the square root of 1 is i, what is the square root of i?
How can you find the log of a negative number?
What is the log of 1?
Answered by Claude Tardif. 





A graph with certain properties 
20041122 

From A student: i was asked as a question in coursework to sketch the graph with the following characteristics:
a double root at 3
a pair of imaginary roots
an xintercept at 6
a root at 4 which is not a double root Answered by Penny Nom. 





Imaginary roots of a ploynomial 
20041031 

From Jennifer: how to find the roots of a polynomial equation if it would be imaginary? Answered by Harley Weston. 





(a+b) + 5i = 9 + ai 
20040625 

From Josh: The question which someone gave you (a+b) + 5i = 9 + ai question) gave me trouble. Answered by Penny Nom. 





3+4i abd 3+4i 
20040617 

From Sandy: how would you do a question like 3+4i? is that different than just doing 3+4i? Answered by Penny Nom. 





z^2 = 3  4i 
20040326 

From John: Solve: Z^2 = 3  4i Answered by Harley Weston. 





A new way to measure randomness 
20031231 

From Stephanie:
Last year, I did a science project in which I asked, "Which shuffles better, an automatic card shuffler or shuffling by hand?" To measure this I decided the "best" shuffler was the one to become random first. Last year, to measure randomness, I numbered cards 152 and had the subjects shuffle them until they broke up the rising sequences or reached 10 shuffles. (Usually 10 shuffles came first...) Anyway, I did the same thing with the automatic card shuffler, and, as hypothesized, the automatic card shuffler randomized the deck first.
This year, I have decided to continue the project. The problem is, I need a new way to measure randomness without the use of fancy computers or something. I have searched the Internet, I have posted my query on websites based on math, and I have searched the local library.
I have found many useful things on the Internet, but none of them can tell me a new way to measure randomness. I cannot do a perfect shuffle, and I am not terribly gifted in the art of using computers. If you have any information (anything will help) or advice, I would be greatly obliged. Answered by Andrei Volodin. 





A triangle in the complex plane 
20030710 

From Scott: The vertices O and A of an EQUILATERAL triangle OAB in the complex plane are located at the origin and 3 + 3i. Find all possible values for the complex number representing the vertex B. Give the location of B in both polar and cartesian form (to 2.d.p) Answered by Penny Nom. 





Real numbers 
20030509 

From Sirena: what is a "real" number Answered by Penny Nom. 





A complex quadratic 
20021006 

From Michael: I would like to know, how to solve this Complex number: quadratic equation. ix^{ 2} + x i = 0 Answered by Harley Weston. 





a+b=10 and ab=40 
20020427 

From April: What two numbers add to ten and multiply to forty? (a+b=10, a*b=40) I think the answer includes radicals and/or imaginary numbers. Answered by Penny Nom. 





The square root of i 
20020314 

From Arlene: what is the square root of i, if i=x+yi? what is the square root of 1i? i'm getting problems like these in which I do not understand. Answered by Harley Weston. 





e^{ix} = cosx + isinx 
20011010 

From Peter: Given: e^{ix} = cosx + isinx  substitute x for x to find e^{ix}, simplifying your answer
 use the given and part a to find an identity for cosx making no reference to trig functions
 find an identity for sinx
 .
 .
Answered by Penny Nom. 





Some complex problems 
20010115 

From Nick: I am having enormous difficulty with one question in my maths homework. The question is shown below. If anybody out there can find the answers and show the workings and help me to understand. Answered by Harley Weston. 





A complex calculation 
20001124 

From Angie: Multiply (32i)^{2}=3^{2}2(3)(2i)+(2i)^{2} Answered by Penny Nom. 





The magnitude of a complex number 
20001111 

From Jeremy: Recently, we started studying how to graph complex numbers. Our math teacher said to use what would normally be the xaxis as the realaxis and to use the yaxis as the imaginaryaxis. However, when he started talking about how to calculate magnitude, that's when I became confused. For instance... Answered by Walter Whiteley. 





Powers of i 
20000524 

From Paul Fieldhouse: What is the result of raising i to the googol power? is there a rule or pattern to raising i by increasing powers of 10? Answered by Penny Nom. 





The square root of 1 
20000519 

From Gary: i am not a student i am just some one that heard something and i can't be sure on the answer...my ? is what is the square root of 1? i think it is 1 but not sure can you let me know please thank you Answered by Harley Weston. 





root(1)* root(1) 
20000320 

From Michael Moran: i squared = 1 but i squared = root(1)* root(1) = root( 1*1) = root(1) = 1 1 doesn't = 1 can you help me with my question Answered by Claude Tardif. 





Complex Roots 
20000124 

From Jess Rutherford: How do I find the value of k when 5x^{2} + k = 3x and has complex roots ? Answered by Penny Nom. 





Complex numbers/polar coordinates 
19990325 

From Kate Cegelis: What is the relationship between complex numbers and polar coordinates? Answered by Harley Weston. 





Absolute value of i 
19990106 

From Wayne Bagley: I would like to know what is the absolute value of i. I need an answer suitable for the secondary level. Answered by Harley Weston. 





Complex numbers and the quadratic formula 
19981225 

From Richard Peter: My age is 16, and my name is Richard. My question relates to the topic complex numbers & the quadratic formula. I would like to know how to solve quadratic equations in which the discriminant is less than 0 (i.e. we get two complex solutions to the quadratic) 3x^{2}+2x+5 = 0 and how mathematicians like euler contributed to this field. If it would be possible I would also like to know how this type of quadratic equations can be graphed? Answered by Harley Weston. 





Complex Numbers 
19981223 

From Wayne Bagley: I would like to know what is the square root of i , and i squared? I am looking for a response appropriate for secondary level students. Answered by Harley Weston. 





Two Problems 
19980728 

From James Pulver: How do you solve these problem? If log abc=16 and log ac=12 , find b. (The logs are log base 10.) and If a and b are real numbers, i^2 = 1 and (a+b)+5i=9+ai what is the value of b? Answered by Jack LeSage. 





Multiplying imaginary numbers. 
19971103 

From Jim Catton: Here is the question: (square root 2) x (square root 8) My algebra suggests two possibilities . . .
Answered by Walter Whiteley, Chris Fisfer and Harley Weston. 





How do you raise a number to an imaginary/complex power? 
19960703 

From Andy Golden: How do you raise a number to an imaginary/complex power? I know how you raise "e" to a complex power, like e^(pi*i): cos pi + i * sin pi But what about numbers other than "e"? What if I want to raise 5 to the 2i power? How is that done? Answered by Chris Fisher. 





Complex numbers 
19951022 

From Jacquie: Why should we teach complex numbers in high school? Answered by Harley Weston. 

