What is the answer to x^2+6xi-9=(5+12i)y ?

The answer to x^2+6xi-9=(5+12i)y is

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x^2+6xi-9=(5+12i)y

x^{2} + 6 x i - 9 = (5 + 12 i) y

(x = \frac{9}{2}, x = - 2, y = \frac{9}{4} y = - 1)

Solution steps

x^{2} + 6 x i - 9 = (5 + 12 i) y

Rewrite

x^{2} + 6 x i - 9

in standard complex form:

(x^{2} - 9) + 6 x i

(x^{2} - 9) + 6 x i = (5 + 12 i) y

Rewrite

(5 + 12 i) y

in standard complex form:

5 y + 12 y i

(x^{2} - 9) + 6 x i = 5 y + 12 y i

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

[x^{2} - 9 = 5 y 6 x = 12 y]

[x^{2} - 9 = 5 y 6 x = 12 y] : (x = \frac{9}{2}, x = - 2, y = \frac{9}{4} y = - 1)

(x = \frac{9}{2}, x = - 2, y = \frac{9}{4} y = - 1)

3 x + 8 i = 12 - 12

x i + y^{2} (1 + i) = 3 - 2 i

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

x^{2} - 8.4 x i - 3.15 = 0

z^{2} + (2 - 12 i) z + (- 1 - 9 i) = 0