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Hi guys! I lost my MathSolver account (I am MathSolver) because I forgot my password -_-. Anyway... This is my new account! Also, I have a question:

Find all complex numbers $z$ such that $z^4 = -4.$


Note: All solutions should be expressed in the form $a+bi$, where $a$ and $b$ are real numbers.

Please explain thoroughly! Goodnight!!

Thanks in advance,

Math Solver

 Dec 8, 2020
 #1
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We replace z^4 with u^2, where u = z^2

u = z^2

y^2 = z^4

u^2 = -4

Then we take the square root of both sides

u = +-sqrt(-4)

u= i*sqrt(4) or u = -i*sqrt(4)

u = 2i or u = -2i

then we can replace u again back with z^2

z^2 = 2i or z^2 = -2i

and then we find square root again

z = 1 + i or z =  -1 - i or z = -1 + i or z = 1 + i

 Dec 8, 2020
 #2
avatar+71 
-1

Thank you so much!!

MathSolverForLYFE  Dec 9, 2020

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