Find all complex numbers such that

Question

z^2=2i. Thank you!

Answer 1

it's easiest to use the polar form

if z = r cisθ
z^2 = r^2 cis2θ
so,

r^2 cis2θ = 2 cis π/2
r = ±√2
θ = π/4

So, we have
√2 cis π/4
-√2 cis π/4

√2/√2 + √2/√2 i = 1+i
or -(1+i)

check:

(1+i)^2 = 1+2i+i^2 = 1+2i-1 = 2i
same for -(1+i)