What is the answer to solvefor x, x/(1-x)=1-5i ?

The answer to solvefor x, x/(1-x)=1-5i is x= 27/29-5/29 i

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solvefor x, x/(1-x)=1-5i

solve for

x, \frac{x}{1 - x} = 1 - 5 i

x = \frac{27}{29} - \frac{5}{29} i

Solution steps

\frac{x}{1 - x} = 1 - 5 i

Substitute

x = a + bi

\frac{a + bi}{1 - ( a + bi )} = 1 - 5 i

Multiply both sides by

1 - a - ib

\frac{a + bi}{1 - ( a + bi )} (1 - a - ib) = 1 \cdot (1 - a - ib) - 5 i (1 - a - ib)

Expand

a + ib = (1 - a - 5 b) + i (- 5 - b + 5 a)

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

[a = 1 - a - 5 b b = - 5 - b + 5 a]

[a = 1 - a - 5 b b = - 5 - b + 5 a] : a = \frac{27}{29}, b = - \frac{5}{29}

Substitute back

x = a + bi

x = \frac{27}{29} - \frac{5}{29} i

(x - y i) + ∣ x + y i ∣ = 25 - 5 i

z^{2} = 5 - 6 i

\frac{( 1 + ai )}{6 + bi} = 1 + 5 i

(3 + i) (a + bi) = (3 - i) (a - bi)

z^{2} - (3 + 4 i) z + 7 i - 1 = 0

What is the answer to solvefor x, x/(1-x)=1-5i ?
The answer to solvefor x, x/(1-x)=1-5i is x= 27/29-5/29 i