What is the answer to (15)/(z-1)=-6-3i ?

The answer to (15)/(z-1)=-6-3i is z=-1+i

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(15)/(z-1)=-6-3i

\frac{15}{z - 1} = - 6 - 3 i

z = - 1 + i

Solution steps

\frac{15}{z - 1} = - 6 - 3 i

Substitute

z = x + y i

\frac{15}{x + y i - 1} = - 6 - 3 i

Multiply both sides by

x - 1 + i y

\frac{15}{x + y i - 1} (x - 1 + i y) = - 6 (x - 1 + i y) - 3 i (x - 1 + i y)

Expand

15 = (- 6 x + 6 + 3 y) + i (3 - 3 x - 6 y)

Rewrite

15

in standard complex form:

15 + 0 i

15 + 0 i = (- 6 x + 6 + 3 y) + i (3 - 3 x - 6 y)

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

[15 = - 6 x + 6 + 3 y 0 = 3 - 3 x - 6 y]

[15 = - 6 x + 6 + 3 y 0 = 3 - 3 x - 6 y] : x = - 1, y = 1

Substitute back

z = x + y i

z = - 1 + i

(x - 2) i = y - 3 i

z^{2} + (2 - 2 i) z - (4 + 2 i) = 0

x + 2 - 3 i y = 0

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

(x + 3) - 3 i = \frac{5 + 3 y i}{2}

What is the answer to (15)/(z-1)=-6-3i ?
The answer to (15)/(z-1)=-6-3i is z=-1+i