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# Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form a + bi. ) (1 - i )2

Find the indicated power using De Moivre's Theorem. (Express your fully simplified answer in the form a + bi. ) (1 − i )2    I need a lot of help on this because its not working for me

### 2 Answers by Expert Tutors

Kevin C. | Successful Math Tutor -- Recently retired high school math teacherSuccessful Math Tutor -- Recently retire...
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DeMoivre's Theorem states:  (a+bi)n = (r cisθ)n = rn cis(nΘ)

r cisθ means r (cosΘ + isinΘ) where r = √(a2 + b2) and θ = arctan(b/a) evaluated in the correct quadrant.

So, in your example, a=1 and b=-1, so r = √2,  and, since a and b are equal in magnitude, and in quadrant IV, we can find θ = 315o or -45o.  (if you are using radians, it would be 7π/4, or -π/4), and n=2.

Therefore, (1-i)2 = (√2)2 cis(2*315o) = 2 cis(630o) = 2 cis(270o) = 2(cos 270o + i sin270o) = 2(0 - i) = -2i.

I hope this helps.

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...
4.8 4.8 (4 lesson ratings) (4)
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You have a parenthesis closed without opening:

a + bi ( 1-i) ^2

a + bi ( 1 -2i - 1) =

a + bi ( 2i) =

a- 2b