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

The answer to ((z-2))/((z+1))=3i is z=-7/10+9/10 i

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((z-2))/((z+1))=3i

\frac{( z - 2 )}{( z + 1 )} = 3 i

z = - \frac{7}{10} + \frac{9}{10} i

Solution steps

\frac{( z - 2 )}{( z + 1 )} = 3 i

Substitute

z = x + y i

\frac{x + y i - 2}{x + y i + 1} = 3 i

Multiply both sides by

x + 1 + i y

\frac{x + y i - 2}{x + y i + 1} (x + 1 + i y) = 3 i (x + 1 + i y)

Simplify

(x - 2) + i y = - 3 y + 3 i (x + 1)

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

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

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

Substitute back

z = x + y i

z = - \frac{7}{10} + \frac{9}{10} i

z^{2} = 8 i

x^{2} - (2 + 3 i) x - 1 + 3 i = 0

(m + ni) (2 + 5 i) = 36 + 3 i

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

z^{2} = 3 i

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