What is the answer to w^2=-40i ?

The answer to w^2=-40i is w=2sqrt(5)-2sqrt(5)i,w=-2sqrt(5)+2sqrt(5)i

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w^2=-40i

w^{2} = - 40 i

w = 25 - 25 i, w = - 25 + 25 i

Solution steps

w^{2} = - 40 i

Substitute

w = x + y i

(x + y i)^{2} = - 40 i

Expand

(x + y i)^{2} : (x^{2} - y^{2}) + 2 i x y

(x^{2} - y^{2}) + 2 i x y = - 40 i

Rewrite

- 40 i

in standard complex form:

0 - 40 i

(x^{2} - y^{2}) + 2 i x y = 0 - 40 i

Complex numbers can be equal only if their real and imaginary parts are equalRewrite as system of equations:

[x^{2} - y^{2} = 0 2 x y = - 40]

[x^{2} - y^{2} = 0 2 x y = - 40] : (x = 25, x = - 25, y = - 25 y = 25)

Substitute back

w = x + y i

w = 25 - 25 i, w = - 25 + 25 i

- \frac{1}{z - i} - 1 - i - z = 0

+ 3 i z^{2} = - 7 + 8 i, z^{1} = 5

∣ z + 2 - i ∣ = 2

(x + y i) + (8 - 5 i) = 4 + 3 i

z = 9 e^{i \frac{4 \cdot π}{3}}

What is the answer to w^2=-40i ?
The answer to w^2=-40i is w=2sqrt(5)-2sqrt(5)i,w=-2sqrt(5)+2sqrt(5)i