Studdy AI Logo
Math  /  Algebra

QuestionWrite the complex number in trigonometric form r(cos⁡θ+isin⁡θ)\mathrm{r}(\boldsymbol{\operatorname { c o s }} \theta+i \boldsymbol{\operatorname { s i n }} \theta), with θ\theta in the interval [0∘,360∘)\left[0^{\circ}, 360^{\circ}\right). −3−3i-3-3 i −3−3i=□(cos⁡□∘+isin⁡□∘)-3-3 i=\square\left(\cos \square^{\circ}+i \boldsymbol{\operatorname { s i n }} \square^{\circ}\right) (Type the value for rr as an exact answer, using radicals as needed. Type the value for θ\theta as an integer or decimal rounded to the nearest tenth as needed.)

Studdy Solution
Determine the angle θ \theta .
The complex number −3−3i-3 - 3i lies in the third quadrant. The reference angle is found using the tangent function:
tan⁡θ=−3−3=1 \tan \theta = \frac{-3}{-3} = 1
The reference angle is 45∘ 45^\circ .
Since the complex number is in the third quadrant, we add 180∘ 180^\circ to the reference angle:
θ=180∘+45∘=225∘ \theta = 180^\circ + 45^\circ = 225^\circ
The trigonometric form of the complex number is:
−3−3i=32(cos⁡225∘+isin⁡225∘) -3 - 3i = 3\sqrt{2} \left( \cos 225^\circ + i \sin 225^\circ \right)

View Full Solution - Free
Was this helpful?

Studdy solves anything!

banner

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

ParentsInfluencer programContactPolicyTerms
TwitterInstagramFacebookTikTokDiscord