What is the answer to (1+ai)/(6+bi)=3+7i ?

The answer to (1+ai)/(6+bi)=3+7i is a= 345/7 ,b= 17/7

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(1+ai)/(6+bi)=3+7i

\frac{1 + ai}{6 + bi} = 3 + 7 i

a = \frac{345}{7}, b = \frac{17}{7}

Solution steps

\frac{1 + ai}{6 + bi} = 3 + 7 i

Multiply both sides by

6 + bi

\frac{1 + ai}{6 + bi} (6 + bi) = 3 (6 + bi) + 7 i (6 + bi)

Expand

1 + ia = (18 - 7 b) + i (42 + 3 b)

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

[1 = 18 - 7 b a = 42 + 3 b]

[1 = 18 - 7 b a = 42 + 3 b] : a = \frac{345}{7}, b = \frac{17}{7}

a = \frac{345}{7}, b = \frac{17}{7}

(1 + i) x - i y = 2 + i, (2 + i) x + (2 - i) y = 2 i

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

(z + i)^{2} = i

i x^{2} + 8 x - 7 i = 0

z - \frac{1}{z} = 3 + 3 i

What is the answer to (1+ai)/(6+bi)=3+7i ?
The answer to (1+ai)/(6+bi)=3+7i is a= 345/7 ,b= 17/7