How do you use demoivre's theorem to simplify (1+i)^{5}?

Maximus George

Maximus George

Answered question

2022-01-31

How do you use demoivre's theorem to simplify (1+i)5?

Answer & Explanation

waijazar1

waijazar1

Beginner2022-02-01Added 13 answers

Solution:
x+iyx2+y2eiϕ
where eiϕ=cos(ϕ)+isin(ϕ)
and ϕ=arctan(yx)
Applying to our example
1+i=2eiπ4 then
(i+1)5=(2eiπ4)5=(2)5ei5π4
but ei5π4=ei4π4eiπ4=eiπ4 and (2)5=42
Answer: (i+1)5=4(i+1)

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