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1.  What is the smallest positive integer value of n such that (sqrt3/2  -   i/2)^n  is real?

 

2. If x + x^-1 = sqrt2, find x^20 

 

3. let z = 3[cos(85) + i*sin(85)]. Find the smallest positive value of r such that   r[cos(45) + i*sin(45)]  = z^n for some positive integer n. 

 Dec 26, 2022
 #1
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1. The smallest n that works is 12.

 

2. x^20 = -3.

 Dec 28, 2022
 #2
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I'm sorry, but those are incorrect... could I also see the work for the solution so I can understand the problem?

Guest Dec 28, 2022
 #3
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3. The smallest r that works is 243.

 Dec 29, 2022

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