How do you find the power (-2+2i)^{3} and express the

derlingasmh

derlingasmh

Answered question

2022-01-30

How do you find the power (2+2i)3 and express the result in rectangular form?

Answer & Explanation

gekraamdbk

gekraamdbk

Beginner2022-01-31Added 13 answers

Step 1
We use polar complex first t o simplify down
Let Reiθ=2+2i
=22(12+i2)
=22(12+i2)
We will find -ve value for cosθ and +ve value for sinθ in Q2 of the Argand diagram.
θ=3π4
Reiθ=22ei3π4
(Reiθ)3=(22)3ei3×π4
=162eiπ4
=16(1+i)
clearly you could also use a binomial expansion

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