Question

Given z = −7 − 3i, rewrite z in trigonometric form. 6.325 (cos 23.199° + isin 23.199°) 7.616(cos 23.199° + isin 23.199°) 6.325(cos 203.199° + isin 203.199°) 7.616(cos 203.199° + isin 203.199°)

Answer 1

7.616(cos 203.199° + i sin 203.199°)

Explanation:

For
`\boxed{z=(Re)+(Im)i}`, the trigonometric form =
`\boxed{r(cos\theta+isin\theta)}`

where:

`\boxed{r=√(Re^2+Im^2) }`

`\boxed{tan\theta=(Im)/(Re) }`

Given:

Re = -7

Im = -3

`r=√((-7)^2+(-3)^2)`

`=7.616`

`tan\theta=(-3)/(-7)`

`\theta=203.199^o` (x and y are negative → Quadrant 3)

Therefore, the trigonometric form =

7.616(cos 203.199° + i sin 203.199°)