What is the answer to 2x+9yi=16-12i ?

The answer to 2x+9yi=16-12i is x=8,y=-4/3

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2x+9yi=16-12i

2 x + 9 y i = 16 - 12 i

x = 8, y = - \frac{4}{3}

Solution steps

2 x + 9 y i = 16 - 12 i

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

[2 x = 16 9 y = - 12]

[2 x = 16 9 y = - 12] : x = 8, y = - \frac{4}{3}

x = 8, y = - \frac{4}{3}

z^{2} = 96 + 40 i

a - ib = - 1 b + ia

z^{2} - 2 i z - 1 - 3 i = 0

∣ z - 2 i ∣ = 1

x^{2} = - 16 + 30 i