What is the answer to (a+ib)^2=-5+12i ?

The answer to (a+ib)^2=-5+12i is

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(a+ib)^2=-5+12i

(a + ib)^{2} = - 5 + 12 i

(a = 2, a = - 2, b = 3 b = - 3)

Solution steps

(a + ib)^{2} = - 5 + 12 i

Expand

(a + ib)^{2} : (a^{2} - b^{2}) + 2 iab

(a^{2} - b^{2}) + 2 iab = - 5 + 12 i

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

[a^{2} - b^{2} = - 5 2 ab = 12]

[a^{2} - b^{2} = - 5 2 ab = 12] : (a = 2, a = - 2, b = 3 b = - 3)

(a = 2, a = - 2, b = 3 b = - 3)

3 x - 5 s i x = - 5

z^{2} - 8 i = 0

(3 - 6 i) (2 - ai) = x

z - 2 x + 7 - 6 i = 0

3 + 8 i = x + y i