







Simplifying a complex expression 
20211215 

From Grace: Write in the form. a+bi,
67i+8i^2+4i35i^4 Answered by Penny Nom. 





0^(a+bi) 
20201203 

From Douglas: I realize raising 0^a = 0 if a>0 and undefined if a<=0.
If have read that 0^bi is undefined for all b.
What I don't understand is why 0^(a+bi) = 0 if a and b are not equal to zero.
Is this purely by definition or is there a logical reason why this is the case?
(I have taken Complex Analysis, so have a fairly good understanding of complex numbers.) Answered by Penny Nom. 





Investigating y = (2)^x 
20200113 

From Gonzalo: This is not precisely a maths question, but it is formulated based on my maths curiosity. Fidgetting with my new graphic calculator, I started graphing things and had the idea to graph $y=(2)^x.$
The result surprised me, and I thought a little bit about it, stored it on the back of my brain, and promised myself to look deeper into it someday. Answered by Harley Weston. 





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. 





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. 





(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. 





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. 





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. 





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. 





z^2 = 3  4i 
20040326 

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





Real numbers 
20030509 

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





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. 





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 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. 





Complex numbers 
19951022 

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

