What is the answer to (3-2i)(x+iy)=2(x-2iy)+2i-1 ?

The answer to (3-2i)(x+iy)=2(x-2iy)+2i-1 is x=-1,y=0

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(3-2i)(x+iy)=2(x-2iy)+2i-1

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

x = - 1, y = 0

Solution steps

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

Expand

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

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

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

[3 x + 2 y = 2 x - 1 - 2 x + 3 y = 2 - 4 y] : x = - 1, y = 0

x = - 1, y = 0

(1 + i) x + (y + 5) i = 3 (1 - y)

(1 - i) x + (1 + i) y = 1 - 3 i

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

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

a - bi = ai - b

What is the answer to (3-2i)(x+iy)=2(x-2iy)+2i-1 ?
The answer to (3-2i)(x+iy)=2(x-2iy)+2i-1 is x=-1,y=0