What is the answer to (3+ai)/(5+bi)=1+6i ?

The answer to (3+ai)/(5+bi)=1+6i is a= 91/3 ,b= 1/3

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(3+ai)/(5+bi)=1+6i

\frac{3 + ai}{5 + bi} = 1 + 6 i

a = \frac{91}{3}, b = \frac{1}{3}

Solution steps

\frac{3 + ai}{5 + bi} = 1 + 6 i

Multiply both sides by

5 + bi

\frac{3 + ai}{5 + bi} (5 + bi) = 1 \cdot (5 + bi) + 6 i (5 + bi)

Simplify

3 + ia = (5 - 6 b) + i (30 + b)

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

[3 = 5 - 6 b a = 30 + b]

[3 = 5 - 6 b a = 30 + b] : a = \frac{91}{3}, b = \frac{1}{3}

a = \frac{91}{3}, b = \frac{1}{3}

- 2 x + 6 i = (- 24 y) i - 14

∣ z - 4 i ∣ = 4

z (z + 1) = 5 + 5 i

2 z^{2} - 2 i z - 1 = 0

i z^{2} + 2 - i = (2 + 2 i) z

What is the answer to (3+ai)/(5+bi)=1+6i ?
The answer to (3+ai)/(5+bi)=1+6i is a= 91/3 ,b= 1/3