What is the answer to (1+ai)/(5+bi)=2+7i ?

The answer to (1+ai)/(5+bi)=2+7i is a= 263/7 ,b= 9/7

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(1+ai)/(5+bi)=2+7i

\frac{1 + ai}{5 + bi} = 2 + 7 i

a = \frac{263}{7}, b = \frac{9}{7}

Solution steps

\frac{1 + ai}{5 + bi} = 2 + 7 i

Multiply both sides by

5 + bi

\frac{1 + ai}{5 + bi} (5 + bi) = 2 (5 + bi) + 7 i (5 + bi)

Expand

1 + ia = (10 - 7 b) + i (35 + 2 b)

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

[1 = 10 - 7 b a = 35 + 2 b]

[1 = 10 - 7 b a = 35 + 2 b] : a = \frac{263}{7}, b = \frac{9}{7}

a = \frac{263}{7}, b = \frac{9}{7}

z - \frac{2}{z} = i + \frac{2}{i}

(2 + i) z^{2} + (1 - 7 i) z - 5 = 0

c, w + i = \frac{s}{c}

6 i - x + y i = 4 + 2 i

∣ z ∣ - z = 2 + i

What is the answer to (1+ai)/(5+bi)=2+7i ?
The answer to (1+ai)/(5+bi)=2+7i is a= 263/7 ,b= 9/7