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

derlingasmh

derlingasmh

Answered

2022-01-30

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

Answer & Explanation

gekraamdbk

gekraamdbk

Expert

2022-01-31Added 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

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?