What is the answer to -2xi+3x-5y-10=-4yi-5x+8i ?

The answer to -2xi+3x-5y-10=-4yi-5x+8i is x= 40/11 ,y= 42/11

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-2xi+3x-5y-10=-4yi-5x+8i

- 2 x i + 3 x - 5 y - 10 = - 4 y i - 5 x + 8 i

x = \frac{40}{11}, y = \frac{42}{11}

Solution steps

- 2 x i + 3 x - 5 y - 10 = - 4 y i - 5 x + 8 i

Rewrite

- 2 x i + 3 x - 5 y - 10

in standard complex form:

(3 x - 5 y - 10) - 2 x i

(3 x - 5 y - 10) - 2 x i = - 4 y i - 5 x + 8 i

Rewrite

- 4 y i - 5 x + 8 i

in standard complex form:

- 5 x + (- 4 y + 8) i

(3 x - 5 y - 10) - 2 x i = - 5 x + (- 4 y + 8) i

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

[3 x - 5 y - 10 = - 5 x - 2 x = - 4 y + 8]

[3 x - 5 y - 10 = - 5 x - 2 x = - 4 y + 8] : x = \frac{40}{11}, y = \frac{42}{11}

x = \frac{40}{11}, y = \frac{42}{11}

z^{2} = - 2 i

3 + y i = x - 7 i

z^{2} - (1 - 2 i) z + (8 + 2 i) = 0

z - \frac{1}{z} = 5 + 4 i

∣ z ∣ - z = 1 + 2 i

What is the answer to -2xi+3x-5y-10=-4yi-5x+8i ?
The answer to -2xi+3x-5y-10=-4yi-5x+8i is x= 40/11 ,y= 42/11