Question 670307: Please help me simplify the two following equations and put the answer into a+bi form:
(a) i^42
(b) (2*cos(pi/12)+2*i*sin(pi/12))^4 Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website! Please help me simplify the two following equations and put the answer into a+bi form:
(a) i^42
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i^1 = i
i^2 = -1
i^3 = -i
i^4 = 1
i^5 = i
i^6 = -1
i^7 = -i
i^8 = 1
etc
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(b) (2*cos(pi/12)+2*i*sin(pi/12))^4
(2*cos(pi/12)+2*i*sin(pi/12))^4 = (2cis(pi/12))^4
= 16cis(pi/3)
= 16 cos(pi/3) + 16i*sin(pi/3)
If you don't know how those work, having the answers won't be a big help.
