What is the answer to (6-5i)/(2+3i)=a+bi ?

The answer to (6-5i)/(2+3i)=a+bi is a=-3/13 ,b=-28/13

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(6-5i)/(2+3i)=a+bi

\frac{6 - 5 i}{2 + 3 i} = a + bi

a = - \frac{3}{13}, b = - \frac{28}{13}

Solution steps

\frac{6 - 5 i}{2 + 3 i} = a + bi

Expand

\frac{6 - 5 i}{2 + 3 i} : - \frac{3}{13} - \frac{28 i}{13}

- \frac{3}{13} - \frac{28 i}{13} = a + bi

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

[- \frac{3}{13} = a - \frac{28}{13} = b]

[- \frac{3}{13} = a - \frac{28}{13} = b] : a = - \frac{3}{13}, b = - \frac{28}{13}

a = - \frac{3}{13}, b = - \frac{28}{13}

x^{2} - y^{2} - 2 y x i = 4 x + 4

x^{2} - 3 x + 1 + 3 i = 0

\frac{3 + ai}{5 + bi} = 2 + 7 i

(2 x + 10) + 9 i = 20 + (5 y - 1) i

7 x - 6 i = 14 + y i

What is the answer to (6-5i)/(2+3i)=a+bi ?
The answer to (6-5i)/(2+3i)=a+bi is a=-3/13 ,b=-28/13