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

The answer to (2-3i)/(2a+bi)=3+2i is a=0,b=-1

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

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

a = 0, b = - 1

Solution steps

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

Multiply both sides by

2 a + bi

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

Expand

2 - 3 i = (6 a - 2 b) + i (3 b + 4 a)

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

[2 = 6 a - 2 b - 3 = 3 b + 4 a]

[2 = 6 a - 2 b - 3 = 3 b + 4 a] : a = 0, b = - 1

a = 0, b = - 1

(x + i y)^{2} = 2 x i

(x + 1) (x + i) = 0

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

i (x) = - 0.01 x^{2} + 10 x + 300

z, z^{2} = 5 - 12 i

What is the answer to (2-3i)/(2a+bi)=3+2i ?
The answer to (2-3i)/(2a+bi)=3+2i is a=0,b=-1