Question

Write the quotient as a complex number 4-3i/-1-4i

Answer 1

Answer: The answer is C (8/17 + 19/17i)

Answer 2

Given :

(4 - 3i)/(-1-4i)

We know that, i² = -1

Multiply the given complex number the conjugate of the denominator.

Now, we have

`(4-3i)/(-1-4i) =(4-3i)/(-1-4i) * (-1+4i)/(-1+4i)\\ \\ = (-4+16i+3i-12i^(2))/(1-4i+4i-16i^(2)) \\ \\ =(8+19i)/(17)`

∴
`(4-3i)/(-1-4i) = (8+19i)/(17) = (8)/(17) + i (19)/(17)`