# How do you perform the operation in trigonometric form (cos5+isin5)(cos20+isin20)?

Jun 19, 2017

$\cos 25 + i \sin 25$

#### Explanation:

$\text{given}$

${z}_{1} = {r}_{1} \left(\cos {\theta}_{1} + i \sin {\theta}_{1}\right) \text{ and }$

${z}_{2} = {r}_{2} \left(\cos {\theta}_{2} + i \sin {\theta}_{2}\right) \text{ then}$

${z}_{1.} {z}_{2} = {r}_{1.} {r}_{2} \left(\cos \left({\theta}_{1} + {\theta}_{2}\right) + i \sin \left({\theta}_{1} + {\theta}_{2}\right)\right)$

$\text{here } {r}_{1} = {r}_{2} = 1 , {\theta}_{1} = 5 , {\theta}_{2} = 20$

$\Rightarrow \left(\cos 5 + i \sin 5\right) \left(\cos 20 + i \sin 20\right)$

$= \cos 25 + i \sin 25$