What is the answer to (4+3i)/(m+ni)=1+2i ?

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

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(4+3i)/(m+ni)=1+2i

\frac{4 + 3 i}{m + ni} = 1 + 2 i

m = 2, n = - 1

Solution steps

\frac{4 + 3 i}{m + ni} = 1 + 2 i

Multiply both sides by

m + ni

\frac{4 + 3 i}{m + ni} (m + ni) = 1 \cdot (m + ni) + 2 i (m + ni)

Simplify

4 + 3 i = (m - 2 n) + i (n + 2 m)

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

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

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

m = 2, n = - 1

5 + 8 i = x + y i

\frac{1 + ai}{7 + bi} = 3 + 5 i

5 (a + bi) + i (a + bi) + 4 = 0

\frac{a}{h} = \frac{- i}{d}

(a + bi) (x - y i) = 2 + 2 i

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