1. Write z = 1 + i in polar form. 2. Using Euler\'s formula, show that f(x) = e^
ID: 2945547 • Letter: 1
Question
1. Write z = 1 + i in polar form.2. Using Euler's formula, show that f(x) = e^ix is periodic with period 2p.
3. Calculate the internal from 0 to 2p e^inx dx where n is an integer.
4. Calculate the internal from 0 to 2p cos^8 (x) dx by writing cos(x) = 1/2 (e^ix + e^-ix).
Hint: Use the previous result in Problem 3 to significantly reduce the amount of work.
5. Calculate the internal from 0 to 2p cos^n (x) dx where n is any odd integer.
Hint: The result follows immediately if you use the ideas of the previous problem. Alternatively, try the substitution x go x - p
Explanation / Answer
1)r=(12+12) = 2
=tan-1(1/1)=/4
z=2(cos/4 + i sin/4)
2)eix= cos x+i sin x
cos x and sin x both are periodic for =2
hence e^ix is periodic with period 2
please ask 1 question at a time
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