What is the answer to (3+2i)(a+bi)+(5+2i)=3-i ?

The answer to (3+2i)(a+bi)+(5+2i)=3-i is a=-12/13 ,b=-5/13

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(3+2i)(a+bi)+(5+2i)=3-i

(3 + 2 i) (a + bi) + (5 + 2 i) = 3 - i

a = - \frac{12}{13}, b = - \frac{5}{13}

Solution steps

(3 + 2 i) (a + bi) + (5 + 2 i) = 3 - i

Expand

(3 + 2 i) (a + bi) + (5 + 2 i) : (3 a - 2 b + 5) + i (2 + 2 a + 3 b)

(3 a - 2 b + 5) + i (2 + 2 a + 3 b) = 3 - i

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

[3 a - 2 b + 5 = 3 2 + 2 a + 3 b = - 1]

[3 a - 2 b + 5 = 3 2 + 2 a + 3 b = - 1] : a = - \frac{12}{13}, b = - \frac{5}{13}

a = - \frac{12}{13}, b = - \frac{5}{13}

x^{2} = - 4 i

(a + bi)^{2} = 1

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

z^{2} - (2 + i 3) z - 5 + i = 0

x^{2} + 4 i \cdot x - 1 = 0

What is the answer to (3+2i)(a+bi)+(5+2i)=3-i ?
The answer to (3+2i)(a+bi)+(5+2i)=3-i is a=-12/13 ,b=-5/13