Extra Problems for Section 10 - University of Arizona
Complex Numbers Name____________________________
1. Perform the following calculations and simplify your final answer:
A. [pic] B. [pic] C. [pic]
2. Express [pic] in the form [pic].
3. Express [pic] in the form [pic].
In problems 4 and 5 you will derive some formulas by computing something in two different ways, expressing each answer using Euler’s formula, and then equating the results. The final step uses the fact that [pic] tells us that [pic] and [pic].
4. A. Use Euler’s formula to rewrite [pic].
B. Use [pic]to rewrite [pic] in the form [pic].
C. Set your answers to parts A and B equal to each other to derive two famous trig identities.
5. A. Use substitution to evaluate [pic]. Rewrite your answer using Euler’s formula.
B. Rewrite [pic]as the sum of two integrals using algebra.
Hint: [pic]
C. Set your answers to parts A and B equal to each other to derive formulas 8 and 9 from the integral table.
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