380_final_checklist[1]

# 380_final_checklist[1] - MATH 380 Final Exam Study Guide...

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

MATH 380 Final Exam Study Guide Spring 2010 Time of exam: Friday 21 May, 8:00 sharp to 10:30 What to bring: pencil, calculator, one sheet of notes (double-sided). Follow the checklists for the midterm exams plus the following items: sin z , cos z , e z , 1 = (1 ± z ) ; simple rational functions products and quotients of the above (at least for several terms) compute residues at poles apply the residue theorem to calculate integrals apply Rouche±s Theorem to count zeroes of polynomials inside a circle Sample exam questions 1. Find each of the following: (a) (2 + 3 i )(4 ± 5 i ) (b) Arg ( ± p 3 + i ) (c) Re( 2 + 3 i 1 ± i ) (d) sin( + i ) (e) the polar form of ± p 3 + i (f) the square roots of i 2. Find all values of (1 + i ) i : 3. Let H = f z 2 C : Re z > 0 g : Describe the images of H under the function f ( z ) = e z and g ( z ) = Log ( z ) : 4. Let f ( z ) = x 2 ± y 2 ± 2 xyi . Find all values of

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 380_final_checklist[1] - MATH 380 Final Exam Study Guide...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online