A community for students.
Here's the question you clicked on:
 0 viewing
iop360
 2 years ago
find all complex numbers z satisfying
z^4 = 16 in the form a+bi
iop360
 2 years ago
find all complex numbers z satisfying z^4 = 16 in the form a+bi

This Question is Closed

ktnguyen1
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1353832796610:dw

ktnguyen1
 2 years ago
Best ResponseYou've already chosen the best response.0dw:1353833084664:dw

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0so is that just 2 solutions? shouldnt i have 4?

yakeyglee
 2 years ago
Best ResponseYou've already chosen the best response.0It does have four solutions.

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0hmm it says the answers are dw:1353818990720:dw

yakeyglee
 2 years ago
Best ResponseYou've already chosen the best response.0If you're familiar with complex exponentials, try this: \(\large z = re^{i \theta} \Rightarrow z^4 = r^4 e^{i(4\theta)} = 16 = 16 e^{i\pi}\) The values that satisfy this are \(\large r=4\) and \(\large \theta = \{\frac{\pi}{4}, \frac{3\pi}{4}, \frac{5\pi}{4}, \frac{7\pi}{4}\}\). Use \(\large e^{i \theta} = \cos \theta + i \sin \theta\) to convert to polar.

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0how did you come up with the angles and value for r=4

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0i tried this method originally but im confused at that part

iop360
 2 years ago
Best ResponseYou've already chosen the best response.0\[16 = r^4e ^{i(4\theta)}\]

yakeyglee
 2 years ago
Best ResponseYou've already chosen the best response.0Sorry...what I meant was \(r = 2\). We are assuming \(r\) to be positive and real, and we want it to correspond to a length of 16 since in the complex plane 16 has length (absolute value) 16=16. The angles are values \(0\le \theta<2\pi\) such that \(4\theta \text{ mod } 2\pi = \pi\).
Ask your own question
Sign UpFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.