What is the answer to W^2=3+4i ?

The answer to W^2=3+4i is W=2+i,W=-2-i

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W^2=3+4i

W^{2} = 3 + 4 i

W = 2 + i, W = - 2 - i

Solution steps

W^{2} = 3 + 4 i

Substitute

W = x + y i

(x + y i)^{2} = 3 + 4 i

Expand

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

(x^{2} - y^{2}) + 2 i x y = 3 + 4 i

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

[x^{2} - y^{2} = 3 2 x y = 4]

[x^{2} - y^{2} = 3 2 x y = 4] : (x = 2, x = - 2, y = 1 y = - 1)

Substitute back

W = x + y i

W = 2 + i, W = - 2 - i

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

∣ z - 1 + i ∣ = 2

x, x^{2} y + sin (y) = c

z^{2} - (5 + i) z + 8 + i = 0

4 i - 10 = 2 x + y i + 8