What is the answer to (2+ai)/(7+bi)=3+6i ?

The answer to (2+ai)/(7+bi)=3+6i is a= 103/2 ,b= 19/6

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

\frac{2 + ai}{7 + bi} = 3 + 6 i

a = \frac{103}{2}, b = \frac{19}{6}

Solution steps

\frac{2 + ai}{7 + bi} = 3 + 6 i

Multiply both sides by

7 + bi

\frac{2 + ai}{7 + bi} (7 + bi) = 3 (7 + bi) + 6 i (7 + bi)

Expand

2 + ia = (21 - 6 b) + i (42 + 3 b)

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

[2 = 21 - 6 b a = 42 + 3 b]

[2 = 21 - 6 b a = 42 + 3 b] : a = \frac{103}{2}, b = \frac{19}{6}

a = \frac{103}{2}, b = \frac{19}{6}

4 x + i (5 x - y) = 2 + i (- 3)

x, \frac{x}{1 - x} = 1 - 5 i

(x - y i) + ∣ x + y i ∣ = 25 - 5 i

z^{2} = 5 - 6 i

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

What is the answer to (2+ai)/(7+bi)=3+6i ?
The answer to (2+ai)/(7+bi)=3+6i is a= 103/2 ,b= 19/6