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

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

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

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

x = \frac{1}{2}, y = - \frac{1}{2}

Solution steps

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

Rewrite

x

in standard complex form:

x + 0 i

x + 0 i = (2 + 3 y) + i (1 - 2 x)

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

[x = 2 + 3 y 0 = 1 - 2 x]

[x = 2 + 3 y 0 = 1 - 2 x] : x = \frac{1}{2}, y = - \frac{1}{2}

x = \frac{1}{2}, y = - \frac{1}{2}

z - \frac{1}{z} = 1 + 3 i

z^{2} + i z = 2 i^{2}

a + ib = (4 + 3 i) (5 - 2 i)

\frac{- 1 + 2 i}{8 i} = a + bi

z^{2} - 8 z + 18 = 8 i

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