Given (4+2i)m-(1-i)n=-9+9i. Find the complex numbers m and n if m is the conjugate of n.

Answer 1

m = a + bi and n = a - bi

So, (4+2i)(a+bi) - (1-i)(a-bi) = (4a + 4bi + 2ai - 2b) - (a -bi -ai -b) = (3a - b) + (3a + 5b)i = -9 + 9i

3a - b = -9 (real part = real part)

3a + 5b = 9 (imaginary part = imaginary part)

Subtract the equations to get -6b = -18

So, b = 3 and a = -2.

m = -2+3i and n = -2-3i.