Got Homework?
Connect with other students for help. It's a free community.
Here's the question you clicked on:
 0 viewing
iop360
Group Title
find all complex numbers z satisfying
z^4 = 16 in the form a+bi
 2 years ago
 2 years ago
iop360 Group Title
find all complex numbers z satisfying z^4 = 16 in the form a+bi
 2 years ago
 2 years ago

This Question is Closed

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

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

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

cinar Group TitleBest ResponseYou've already chosen the best response.0
dw:1353825968940:dw
 2 years ago

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

cinar Group TitleBest ResponseYou've already chosen the best response.0
dw:1353826101375:dw
 2 years ago

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

yakeyglee Group TitleBest ResponseYou've already chosen the best response.0
If 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.
 2 years ago

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

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

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

yakeyglee Group TitleBest ResponseYou've already chosen the best response.0
Sorry...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 \(4\theta \text{ mod } 2\pi = \pi\).
 2 years ago
See more questions >>>
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.