What is the answer to (a+bi)^2=-16-30i ?

The answer to (a+bi)^2=-16-30i is

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(a+bi)^2=-16-30i

(a + bi)^{2} = - 16 - 30 i

(a = - 3, a = 3, b = 5 b = - 5)

Solution steps

(a + bi)^{2} = - 16 - 30 i

Expand

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

(a^{2} - b^{2}) + 2 iab = - 16 - 30 i

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

[a^{2} - b^{2} = - 16 2 ab = - 30]

[a^{2} - b^{2} = - 16 2 ab = - 30] : (a = - 3, a = 3, b = 5 b = - 5)

(a = - 3, a = 3, b = 5 b = - 5)

\frac{2 + ai}{6 + bi} = 2 + 7 i

z^{2} - (1 + 4 i) z + 3 + 11 i = 0

x + 7 y i - 4 = 5 + 21 i + 2

(x + i y)^{2} + (x + i y) + 1 = 0

A = P (1 + \frac{i}{100})^{2}, i