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

The answer to (3+ai)/(5+bi)=3+5i is a= 161/5 ,b= 12/5

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

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

a = \frac{161}{5}, b = \frac{12}{5}

Solution steps

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

Multiply both sides by

5 + bi

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

Expand

3 + ia = (15 - 5 b) + i (25 + 3 b)

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

[3 = 15 - 5 b a = 25 + 3 b]

[3 = 15 - 5 b a = 25 + 3 b] : a = \frac{161}{5}, b = \frac{12}{5}

a = \frac{161}{5}, b = \frac{12}{5}

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

x, (x + y)^{2} = 3 - 4 i

z^{2} = 3 + 3 i

z^{2} = i (1 - 0. 5^{2})

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

What is the answer to (3+ai)/(5+bi)=3+5i ?
The answer to (3+ai)/(5+bi)=3+5i is a= 161/5 ,b= 12/5