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

The answer to (3b-2ai)/(4-3i)=1 is a= 3/2 ,b= 4/3

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(3b-2ai)/(4-3i)=1

\frac{3 b - 2 ai}{4 - 3 i} = 1

a = \frac{3}{2}, b = \frac{4}{3}

Solution steps

\frac{3 b - 2 ai}{4 - 3 i} = 1

Multiply both sides by

4 - 3 i

\frac{3 b - 2 ai}{4 - 3 i} (4 - 3 i) = 1 \cdot (4 - 3 i)

Simplify

3 b - 2 ia = 4 - 3 i

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

[3 b = 4 - 2 a = - 3]

[3 b = 4 - 2 a = - 3] : a = \frac{3}{2}, b = \frac{4}{3}

a = \frac{3}{2}, b = \frac{4}{3}

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

(x - y) + 3 i = 7 + y i

(3 + 3 i) (x + y i) = 27 - 3 i

(4 + 2 i) (3 - i) = a + bi

z^{2} + (2 i - 3) z + (5 - i) = 0

What is the answer to (3b-2ai)/(4-3i)=1 ?
The answer to (3b-2ai)/(4-3i)=1 is a= 3/2 ,b= 4/3