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

The answer to (1+ai)/(6+bi)=1+5i is a=31,b=1

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

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

a = 31, b = 1

Solution steps

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

Multiply both sides by

6 + bi

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

Simplify

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

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

[1 = 6 - 5 b a = 30 + b]

[1 = 6 - 5 b a = 30 + b] : a = 31, b = 1

a = 31, b = 1

0 = \frac{1 + λi}{1 - λi}

z^{2} - (1 - 2 i) z + (2 - 16 i) = 0

(8 + 9 i) y - (3 + 6 i) x = 16 - 3 i

(5 - 3 i) y - (6 + 2 i) x = 3 - 41 i

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

What is the answer to (1+ai)/(6+bi)=1+5i ?
The answer to (1+ai)/(6+bi)=1+5i is a=31,b=1