What is the answer to 2y+iy=3i+ix-x ?

The answer to 2y+iy=3i+ix-x is x=-2,y=1

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2y+iy=3i+ix-x

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

x = - 2, y = 1

Solution steps

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

Rewrite

3 i + i x - x

in standard complex form:

- x + (3 + x) i

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

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

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

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

x = - 2, y = 1

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

x^{2} - i = 0

(2 + x i) + (y + 3 i) = 7 + 4 i

(a + bi)^{2} = 3 + 4 i

∣ z - i ∣ = 1