What is the answer to (2+ai)/(6+bi)=2+7i ?

The answer to (2+ai)/(6+bi)=2+7i is a= 314/7 ,b= 10/7

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(2+ai)/(6+bi)=2+7i

\frac{2 + ai}{6 + bi} = 2 + 7 i

a = \frac{314}{7}, b = \frac{10}{7}

Solution steps

\frac{2 + ai}{6 + bi} = 2 + 7 i

Multiply both sides by

6 + bi

\frac{2 + ai}{6 + bi} (6 + bi) = 2 (6 + bi) + 7 i (6 + bi)

Expand

2 + ia = (12 - 7 b) + i (42 + 2 b)

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

[2 = 12 - 7 b a = 42 + 2 b]

[2 = 12 - 7 b a = 42 + 2 b] : a = \frac{314}{7}, b = \frac{10}{7}

a = \frac{314}{7}, b = \frac{10}{7}

z^{2} - (1 + 4 i) z + 3 + 11 i = 0

x + 7 y i - 4 = 5 + 21 i + 2

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

A = P (1 + \frac{i}{100})^{2}, i

z^{2} = 1 + i + \frac{58}{9 ( 3 - 7 i )}

What is the answer to (2+ai)/(6+bi)=2+7i ?
The answer to (2+ai)/(6+bi)=2+7i is a= 314/7 ,b= 10/7