{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Quiz3solns - 1 e-i π 4 = e cos-π 4 ie sin-π 4 = e √ 2...

Info icon This preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
Quiz 3 Solutions Math 322, Fall 2009 September, 11 2009. NAME: Instructor: Bole Yang, Erica McEvoy Please show ALL of your work. 1. Find the principal value of Ln ( z ) when z = 2 i. Rewrite z into polar form, so that z = 2 e i ( π 2 +2 π n ) . Then Ln ( z ) = ln ( r ) + iArg ( z ) = ln (2) + i π 2 . (Since Arg (2 i ) = π 2 ). 2. Consider the following complex number z = 1 - π 4 i. (a) Write e z in the form u + iv . Use Euler’s formula to simplify e z : e 1 - π 4 i
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 1 e-i π 4 = e cos (-π 4 ) + ie sin (-π 4 ) = e √ 2 2 + ie √ 2 2 . So u = e √ 2 2 and v = e √ 2 2 . MATH 322. QUIZ 2 ———————————————————————————— 2 (b) Find | e z | . The modulus is just √ u 2 + v 2 = ± ( e √ 2 2 ) 2 + ( e √ 2 2 ) 2 = √ e 2 = e ....
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern