What is the answer to (4m-2i)/(3+ni)=6-2i ?

The answer to (4m-2i)/(3+ni)=6-2i is m= 29/6 ,n= 2/3

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(4m-2i)/(3+ni)=6-2i

\frac{4 m - 2 i}{3 + ni} = 6 - 2 i

m = \frac{29}{6}, n = \frac{2}{3}

Solution steps

\frac{4 m - 2 i}{3 + ni} = 6 - 2 i

Multiply both sides by

3 + ni

\frac{4 m - 2 i}{3 + ni} (3 + ni) = 6 (3 + ni) - 2 i (3 + ni)

Expand

4 m - 2 i = (18 + 2 n) + i (- 6 + 6 n)

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

[4 m = 18 + 2 n - 2 = - 6 + 6 n]

[4 m = 18 + 2 n - 2 = - 6 + 6 n] : m = \frac{29}{6}, n = \frac{2}{3}

m = \frac{29}{6}, n = \frac{2}{3}

(x^{2} + 6) + (2 x) i = 15 + 6 i

z^{2} - (1 + 6 i) z - 10 = 0

\frac{48 - 12 i}{x} = 16 - 4 i

y, (2 x - y) - 12 i = 12 + 6

x + 3 y + (2 x - 3 y - 9) i = 0

What is the answer to (4m-2i)/(3+ni)=6-2i ?
The answer to (4m-2i)/(3+ni)=6-2i is m= 29/6 ,n= 2/3