What is the answer to 15-3yi= 1/2 x+2i ?

The answer to 15-3yi= 1/2 x+2i is x=30,y=-2/3

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15-3yi= 1/2 x+2i

15 - 3 y i = \frac{1}{2} x + 2 i

x = 30, y = - \frac{2}{3}

Solution steps

15 - 3 y i = \frac{1}{2} x + 2 i

Rewrite

\frac{1}{2} x + 2 i

in standard complex form:

\frac{x}{2} + 2 i

15 - 3 y i = \frac{x}{2} + 2 i

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

[15 = \frac{x}{2} - 3 y = 2]

[15 = \frac{x}{2} - 3 y = 2] : x = 30, y = - \frac{2}{3}

x = 30, y = - \frac{2}{3}

(9 x + 8 y) + i (12 x - 6 y) = 10 + 10 i

z^{2} = - 1 + 3 i

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

x, z = \frac{x + 4 i}{1 - x i}

\frac{z - 1}{z} = 2 + i

What is the answer to 15-3yi= 1/2 x+2i ?
The answer to 15-3yi= 1/2 x+2i is x=30,y=-2/3