SOLUTION: Find all complex numbers z such that z^2 = 2i. Write your solutions in a+bi form, separated by commas. So, "1+2i, 3-i" is an acceptable answer format, but "2i+1; -i+3" is not. (

Question 1028076: Find all complex numbers z such that z^2 = 2i.
Write your solutions in a+bi form, separated by commas. So, "1+2i, 3-i" is an acceptable answer format, but "2i+1; -i+3" is not. (Don't include quotes in your answer.)
Note: This problem is not about functions.
Found 2 solutions by Alan3354, richard1234:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
Find all complex numbers z such that z^2 = 2i.
------------
z^2 = 2cis90
z = sqrt(2)cis(45), sqrt(2)cis(225)
----
z = sqrt(2)*sqrt(2)/2 + isqrt(2)*sqrt(2)/2
= 1 + i
=====================
z = sqrt(2)cis(225)
sqrt(2)*(-sqrt(2)/2) + i*sqrt(2)*(-sqrt(2)/2)
= -1 - i

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
Use the fact that

Since you can conclude that the magnitude of z is .

Then you can conclude that and are the solutions. Since the equation is quadratic, it must have at most two complex solutions, including multiple roots.
RELATED QUESTIONS
Find all complex numbers z such that z^2 = 2i. Write your solutions in a+bi form,... (answered by Fombitz)
Find all complex numbers z such that |z - 1| = |z + 3| + |z - 2i|. (answered by CPhill,ikleyn)
Find all complex numbers $z$ such that $|z-1|=|z+3|=|z-i|$. Express each answer in the (answered by Fombitz,ikleyn)
Find all complex numbers z such that... (answered by jim_thompson5910)
if z/3+2i=5-2i, how do you find z in a+bi... (answered by richwmiller)
Find the complex number z = a + bi such that z^3= 2 + 2i where a is less than or equal to (answered by jim_thompson5910)
Find all complex numbers z such that |z| ^ 2 - 2 z + iz = 2i. The second 2 has an... (answered by Edwin McCravy)
please help Write each complex number in standard form a + bi showing all work a)... (answered by Nate)
I'm needing your help on the following: For z = 8 - i and w = 1 - 2i, find z/w. That... (answered by Alan3354)