What is the answer to (a+2i)/(3+bi)=4-3i ?

The answer to (a+2i)/(3+bi)=4-3i is a= 81/4 ,b= 11/4

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

\frac{a + 2 i}{3 + bi} = 4 - 3 i

a = \frac{81}{4}, b = \frac{11}{4}

Solution steps

\frac{a + 2 i}{3 + bi} = 4 - 3 i

Multiply both sides by

3 + bi

\frac{a + 2 i}{3 + bi} (3 + bi) = 4 (3 + bi) - 3 i (3 + bi)

Expand

a + 2 i = (12 + 3 b) + i (- 9 + 4 b)

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

[a = 12 + 3 b 2 = - 9 + 4 b]

[a = 12 + 3 b 2 = - 9 + 4 b] : a = \frac{81}{4}, b = \frac{11}{4}

a = \frac{81}{4}, b = \frac{11}{4}

2 y - 3 + (4 x + 8) i = 0

i (x + y i) = (1 - 6 i) (2 + 3 i)

(a - 2 i)^{2} = 21 - 20 i

x, i = k + \frac{b - x}{x}

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

What is the answer to (a+2i)/(3+bi)=4-3i ?
The answer to (a+2i)/(3+bi)=4-3i is a= 81/4 ,b= 11/4