Let z=e^{it}+1 where 0\leq t\leq\pi, Find the trigonometric representation of

Casertowm7

Casertowm7

Answered question

2022-02-27

Let z=eit+1 where 0tπ, Find the trigonometric representation of z2+z+1

Answer & Explanation

Balraj Conrad

Balraj Conrad

Beginner2022-02-28Added 9 answers

A different strategy, possibly a little more simple:
a3b3=(ab)(a2+ab+b2)a2+ab+b2=a3b3ab
Well, just put a=z, b=1 above, and get
z2+z+1=z31z1
and since z=eit+1, we get
z2+z+1=(eit+1)31eit=e2it+3eit+3
=(cos2t+3cost+3)+(sin2t+3sint)i

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