What is the answer to (a+bi-2)/(a+bi+1)=3i ?

The answer to (a+bi-2)/(a+bi+1)=3i is a=-7/10 ,b= 9/10

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(a+bi-2)/(a+bi+1)=3i

\frac{a + bi - 2}{a + bi + 1} = 3 i

a = - \frac{7}{10}, b = \frac{9}{10}

Solution steps

\frac{a + bi - 2}{a + bi + 1} = 3 i

Multiply both sides by

a + 1 + ib

\frac{a + bi - 2}{a + bi + 1} (a + 1 + ib) = 3 i (a + 1 + ib)

Simplify

(a - 2) + ib = - 3 b + 3 i (a + 1)

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

[a - 2 = - 3 b b = 3 a + 3]

[a - 2 = - 3 b b = 3 a + 3] : a = - \frac{7}{10}, b = \frac{9}{10}

a = - \frac{7}{10}, b = \frac{9}{10}

a + bi = 8 i

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

i (x) = \frac{x ^{2} - 16}{x - 6}

(4 + 2 i) (x + y i) = 32 + 6 i

r (t) = t + 5 i + t - 7 j

What is the answer to (a+bi-2)/(a+bi+1)=3i ?
The answer to (a+bi-2)/(a+bi+1)=3i is a=-7/10 ,b= 9/10