A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
considering the equation cos(z)=4, z being a complex variable, how can I solve it?
sorry for posting here, but supposed I could get some help here.
 2 years ago
considering the equation cos(z)=4, z being a complex variable, how can I solve it? sorry for posting here, but supposed I could get some help here.

This Question is Open

hellow
 2 years ago
Best ResponseYou've already chosen the best response.1I think I found the answer online. It is posted here: http://www.freemathhelp.com/forum/threads/58401Usecos%28Z%29%28eizeiz%292tosolvecos%28Z%294. It turns out you can use the definition of the cosine of a complex number, and then use the quadratic equation to solve for e^(iz). Once you have found e^(iz), you can find z.

pjcappaert
 2 years ago
Best ResponseYou've already chosen the best response.0Hellow, how exactly do you make e^iz+e^iz=8 into a quadratic equation?

hellow
 2 years ago
Best ResponseYou've already chosen the best response.1We can set x=e^(iz) in \[e ^{iz}+(e ^{iz})^{1}=8\] So then we have x+x^1=8. So we get (multiplying both sides by x): x^2+1=8x (quadratic!) x^28x+1=0 \[x=((8)\pm \sqrt{644})/2=4\pm2\sqrt{15}\] So e^(iz) = 4+/ 2sqrt(15). From there I think you can take the natural log of both sides, then divide both sides by i: iz=ln(4+/2sqrt(15)) z=1/iln(4+/sqrt(15)) = 1/i(i/i)ln(4+/sqrt(15)) = iln(4+/sqrt(15)) (If you don't want to convert the e^(iz) to x, you can also work with the coefficients of \[e ^{2iz}8e ^{iz}+1=0\] and and use the quadratic equation to find e^iz.)

pjcappaert
 2 years ago
Best ResponseYou've already chosen the best response.0Damn that was too easy. Thanks
Ask your own question
Ask a QuestionFind 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.