What is the answer to (-4+mi)/(2-3i)=n-2i ?

The answer to (-4+mi)/(2-3i)=n-2i is n=1,m=-7

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(-4+mi)/(2-3i)=n-2i

\frac{- 4 + mi}{2 - 3 i} = n - 2 i

n = 1, m = - 7

Solution steps

\frac{- 4 + mi}{2 - 3 i} = n - 2 i

Multiply both sides by

2 - 3 i

\frac{- 4 + mi}{2 - 3 i} (2 - 3 i) = n (2 - 3 i) - 2 i (2 - 3 i)

Expand

- 4 + im = (2 n - 6) + i (- 4 - 3 n)

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

[- 4 = 2 n - 6 m = - 4 - 3 n]

[- 4 = 2 n - 6 m = - 4 - 3 n] : n = 1, m = - 7

n = 1, m = - 7

3 x + y + (2 x + 2 y) i = 13

\frac{x ^{2} - 5}{2 x + i} = 0

2 x + 2 y = 2 x + 2 y i + 10

2 (a + ib)^{2} + 2 (a + ib) + 13 = 0

R, ii R + i q = e

What is the answer to (-4+mi)/(2-3i)=n-2i ?
The answer to (-4+mi)/(2-3i)=n-2i is n=1,m=-7