How do you divide (-7-7i)/(-7-4i)?

Jan 21, 2017

For a complex number in this form, you need to multiply the numerator and denominator by the conjugate of the denominator: $- 7 + 4 i$

Explanation:

$\frac{\left(- 7 - 7 i\right) \left(- 7 + 4 i\right)}{\left(- 7 - 4 i\right) \left(- 7 + 4 i\right)}$
This will have the effect of eliminating the imaginary numbers in the denominator!
$\left(49 - 28 i + 49 i - 28 {i}^{2}\right)$=$49 + 28 + 21 i$ = $77 + 21 i$ for the numerator.

$49 - 28 i + 28 i - 16 {i}^{2}$ = $49 + 16$ = 65 for the denominator.
Final answer: $\frac{77 + 21 i}{65}$.
Some textbooks require "a+bi" form: $\frac{77}{65} + \frac{21 i}{65}$