What is the answer to (a+2i)(1+2i)=4-bi ?

The answer to (a+2i)(1+2i)=4-bi is a=8,b=-18

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(a+2i)(1+2i)=4-bi

(a + 2 i) (1 + 2 i) = 4 - bi

a = 8, b = - 18

Solution steps

(a + 2 i) (1 + 2 i) = 4 - bi

Expand

(a + 2 i) (1 + 2 i) : (a - 4) + i (2 + 2 a)

(a - 4) + i (2 + 2 a) = 4 - bi

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

[a - 4 = 4 2 + 2 a = - b]

[a - 4 = 4 2 + 2 a = - b] : a = 8, b = - 18

a = 8, b = - 18

z^{2} - \frac{2 i + 1}{2 - i} = 0

∣ x + y i ∣ = y - i x

\frac{( z - 2 i )}{( z + 2 )} = 4 i

- y + x i = x - y i

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

What is the answer to (a+2i)(1+2i)=4-bi ?
The answer to (a+2i)(1+2i)=4-bi is a=8,b=-18