What is the answer to (3-2i)/(i-1)=(2-zi)/(4i) ?

The answer to (3-2i)/(i-1)=(2-zi)/(4i) is z=10

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(3-2i)/(i-1)=(2-zi)/(4i)

\frac{3 - 2 i}{i - 1} = \frac{2 - z i}{4 i}

z = 10

Solution steps

\frac{3 - 2 i}{i - 1} = \frac{2 - z i}{4 i}

Switch sides

\frac{2 - z i}{4 i} = \frac{3 - 2 i}{i - 1}

Apply complex arithmetic rule:

\frac{a + bi}{c + d i} = \frac{( c - d i ) ( a + bi )}{( c - d i ) ( c + d i )} = \frac{( a c + b d ) + ( b c - a d ) i}{c ^{2} + d ^{2}}

a = 3, b = - 2, c = - 1, d = 1

\frac{2 - z i}{4 i} = \frac{( 3 ( - 1 ) + ( - 2 ) \cdot 1 ) + ( - 2 ( - 1 ) - 3 \cdot 1 ) i}{( - 1 ) ^{2} + 1 ^{2}}

Refine

\frac{2 - z i}{4 i} = \frac{- 5 - i}{2}

Multiply both sides by

4 i

2 - i z = 2 - 10 i

Move

2

to the right side

- i z = - 10 i

Divide both sides by

- i

z = 10

(3 x + 2) + (x + 1) = (2 x + 4) + (x + 3)

x, y = 3 f

2 x^{2} - (x + 1)^{2} + 3 x = x (x - 2) + 5

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

- 46 = 4 y - 5 (y + 7)

What is the answer to (3-2i)/(i-1)=(2-zi)/(4i) ?
The answer to (3-2i)/(i-1)=(2-zi)/(4i) is z=10