What is the answer to (-4+xi)/(2-3i)=y-2i ?

The answer to (-4+xi)/(2-3i)=y-2i is x=-7,y=1

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(-4+xi)/(2-3i)=y-2i

\frac{- 4 + x i}{2 - 3 i} = y - 2 i

x = - 7, y = 1

Solution steps

\frac{- 4 + x i}{2 - 3 i} = y - 2 i

Multiply both sides by

2 - 3 i

\frac{- 4 + x i}{2 - 3 i} (2 - 3 i) = y (2 - 3 i) - 2 i (2 - 3 i)

Expand

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

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

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

[- 4 = 2 y - 6 x = - 4 - 3 y] : x = - 7, y = 1

x = - 7, y = 1

3 x - 2 i y - i x + 5 y = 7 + 5 i

x + i y = ∣ x - i y ∣

\frac{4 + x i}{2 + i} = y + 2 i

(a - 1) + (b + 3) i = 5 + 8 i

(x - i y)^{2} = 4 (x + i y)

What is the answer to (-4+xi)/(2-3i)=y-2i ?
The answer to (-4+xi)/(2-3i)=y-2i is x=-7,y=1