What is the answer to (2-2i)/4 =(1-2i)/z ?

The answer to (2-2i)/4 =(1-2i)/z is z=3-i

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(2-2i)/4 =(1-2i)/z

\frac{2 - 2 i}{4} = \frac{1 - 2 i}{z}

z = 3 - i

Solution steps

\frac{2 - 2 i}{4} = \frac{1 - 2 i}{z}

Substitute

z = x + y i

\frac{2 - 2 i}{4} = \frac{1 - 2 i}{x + y i}

Apply fraction cross multiply: if

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

then

a \cdot d = b \cdot c

(2 - 2 i) (x + y i) = 4 (1 - 2 i)

Expand

(2 x + 2 y) + i (- 2 x + 2 y) = 4 - 8 i

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

[2 x + 2 y = 4 - 2 x + 2 y = - 8]

[2 x + 2 y = 4 - 2 x + 2 y = - 8] : x = 3, y = - 1

Substitute back

z = x + y i

z = 3 - i

i z + (1 + 2 i) w = 25

x^{2} + 6 + (2 x) i = 15 + 6 i

i = \frac{70 \cdot 10 e ^{- 9}}{5 s}

e = \frac{( i \cdot n ^{2} )}{( 179 )}

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

What is the answer to (2-2i)/4 =(1-2i)/z ?
The answer to (2-2i)/4 =(1-2i)/z is z=3-i