What is the answer to (2x-3yi)(1-2i)=1-4i ?

The answer to (2x-3yi)(1-2i)=1-4i is x= 9/10 ,y= 2/15

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(2x-3yi)(1-2i)=1-4i

(2 x - 3 y i) (1 - 2 i) = 1 - 4 i

x = \frac{9}{10}, y = \frac{2}{15}

Solution steps

(2 x - 3 y i) (1 - 2 i) = 1 - 4 i

Expand

(2 x - 3 y i) (1 - 2 i) : (2 x - 6 y) + i (- 3 y - 4 x)

(2 x - 6 y) + i (- 3 y - 4 x) = 1 - 4 i

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

[2 x - 6 y = 1 - 3 y - 4 x = - 4]

[2 x - 6 y = 1 - 3 y - 4 x = - 4] : x = \frac{9}{10}, y = \frac{2}{15}

x = \frac{9}{10}, y = \frac{2}{15}

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

(1 + 2 i) (x + y i) - (1 + 2 i) (x - y i) = 16

z^{2} = - 4 i

z^{2} + 2 - 4 i = 0

(x + y i) (2 + i) = 3 - i

What is the answer to (2x-3yi)(1-2i)=1-4i ?
The answer to (2x-3yi)(1-2i)=1-4i is x= 9/10 ,y= 2/15