# How do you divide ( i-1) / (i -2 ) in trigonometric form?

Apr 10, 2016

$C = \frac{3 - i}{3} = 1 - \frac{i}{3}$

#### Explanation:

Given: $C = {C}_{n} / {C}_{d} = \frac{- 1 + i}{- 2 + i}$
Required: The resultant to ${C}_{n} / {C}_{d}$
Solution Strategy: Multiply both nominator and denominator by complex conjugate of the denominator, ${C}_{d} = - 2 + i$.
Complex conjugate of ${C}_{d}^{\text{*}} = \left(- 2 - i\right)$
Thus:
$C = \left({C}_{n} \circ {C}_{d}^{\text{*")/(C_d@C_d^"*}}\right) = \frac{\left(- 1 + i\right) \circ \left(- 2 - i\right)}{\left(- 2 + i\right) \circ \left(- 2 - i\right)}$
$C = \frac{3 - i}{3} = 1 - \frac{i}{3}$