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

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

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(3-i)/z =4+2i

\frac{3 - i}{z} = 4 + 2 i

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

Solution steps

\frac{3 - i}{z} = 4 + 2 i

Substitute

z = x + y i

\frac{3 - i}{x + y i} = 4 + 2 i

Multiply both sides by

x + y i

\frac{3 - i}{x + y i} (x + y i) = 4 (x + y i) + 2 i (x + y i)

Expand

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

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

[3 = 4 x - 2 y - 1 = 2 x + 4 y]

[3 = 4 x - 2 y - 1 = 2 x + 4 y] : x = \frac{1}{2}, y = - \frac{1}{2}

Substitute back

z = x + y i

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

t, a = \frac{v f - v i}{t}

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

∣ z ∣ - 3 z = 1 - 3 i

z^{2} = 5 - 12 i

z^{2} - i z + 2 = 0

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