+71 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
+256 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
