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

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

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

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

x = 1 + 2 i

Solution steps

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

Substitute

x = a + bi

\frac{a + bi - 3}{a + bi + 1} = i

Multiply both sides by

a + 1 + ib

\frac{a + bi - 3}{a + bi + 1} (a + 1 + ib) = i (a + 1 + ib)

Simplify

(a - 3) + ib = - b + i (a + 1)

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

[a - 3 = - b b = a + 1]

[a - 3 = - b b = a + 1] : a = 1, b = 2

Substitute back

x = a + bi

x = 1 + 2 i

\frac{2 - 5 i}{4 - 7 i} = \frac{a}{b}

3 i z^{2} + (8 - 6 i) z - (8 - 6 i) = 0

b (a + bi) + (2 - i) = 3 + i

∣ z + 1 - 3 i ∣ = 2

2 y i + x = 3 - 2 i