







x^2 = 16 
20161212 

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





i^i 
20101121 

From trale: Can we use e^ix=cosx+isinx for finding i^i like that: x= pi/2 =>
e^(ipi/2)=0+i then [e^(ipi/2)]^i=i^i.then we find i^i= 0,207879576....
is it true? can we give value for x for free?thank you. Answered by Harley Weston. 





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. 





A quadratic equation with imaginary numbers 
20100603 

From Alissa: I am solving a quadratic equation and I got this far;
(x4+i)(x4i)=0
but how do I add the imaginary numbers
i know you multiply x by x and then add 4 + 4 but what do you do with the i's? 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. 





Factor 9x^2 + 6x + 4 
20081121 

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





Real and imaginary zeros 
20081112 

From David: Find all the real and imaginary zeros for each polynomial. Factor each polynomial. Leave factors with imaginary zeros in quadratic form.
h(x)= x^5 +2x^4  10x^3 20x^2 +9x + 18 Answered by Harley Weston. 





A quadratic 
20081027 

From Giselle: 3x squared minus 2x equals 5 Answered by Penny Nom. 





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. 





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. 





Simplifying complex denominators 
20070621 

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





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. 





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. 





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. 





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. 





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. 





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. 

