What is the answer to (2+ai)/(4+bi)=2+5i ?

The answer to (2+ai)/(4+bi)=2+5i is a= 112/5 ,b= 6/5

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(2+ai)/(4+bi)=2+5i

\frac{2 + ai}{4 + bi} = 2 + 5 i

a = \frac{112}{5}, b = \frac{6}{5}

Solution steps

\frac{2 + ai}{4 + bi} = 2 + 5 i

Multiply both sides by

4 + bi

\frac{2 + ai}{4 + bi} (4 + bi) = 2 (4 + bi) + 5 i (4 + bi)

Expand

2 + ia = (8 - 5 b) + i (20 + 2 b)

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

[2 = 8 - 5 b a = 20 + 2 b]

[2 = 8 - 5 b a = 20 + 2 b] : a = \frac{112}{5}, b = \frac{6}{5}

a = \frac{112}{5}, b = \frac{6}{5}

w = \frac{p + 4 i}{1 + i p}

25 x^{2} + 60 x + 37 = 0 a + bia + bi

∣ Z + 1 ∣ = (Z + 2) (1 + i)

1 + 2 i = z + \frac{i}{z}

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

What is the answer to (2+ai)/(4+bi)=2+5i ?
The answer to (2+ai)/(4+bi)=2+5i is a= 112/5 ,b= 6/5