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

The answer to 3/(x-yi)=(1+i)/(2-i) is x= 3/2 ,y= 9/2

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3/(x-yi)=(1+i)/(2-i)

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

x = \frac{3}{2}, y = \frac{9}{2}

Solution steps

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

Apply fraction cross multiply: if

\frac{a}{b} = \frac{c}{d}

then

a \cdot d = b \cdot c

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

Expand

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

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

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

[6 = x + y - 3 = x - y] : x = \frac{3}{2}, y = \frac{9}{2}

x = \frac{3}{2}, y = \frac{9}{2}

4 x i + 3 y - 3 = x + 5 i - 8

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

z^{2} + 16 = 30 i

- 2 i e z^{2} = - 1 + i, z^{1} = 3

(i) x^{2} - 16 = 0, (ii) 6 x^{2} - 24 = 0

What is the answer to 3/(x-yi)=(1+i)/(2-i) ?
The answer to 3/(x-yi)=(1+i)/(2-i) is x= 3/2 ,y= 9/2