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lll030lll

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**Patterns found in complex numbers URGENT!**

- use de moivre's theorem to obtain solutions to z^n = i for n=3, 4, 5
- generalise and prove your results for z^n = 1+bi, where |a+bi|=1
- what happens when |a+bi|≠1?

Relevant equations[/b]

r = √a^2 + b^2

z^n = r^n cis (nθ)

This is what i have done:

z^3=i

z^3=i cis(0)

z^3=cis(π/2+2kπ),k=0,1,2

z=cis(π/6+2kπ/3),k=0,1,2

z=cis(π/6),cis(π/6+2π/3),cis(π/6+4π/3)

z=√3/2+0.5i,-√3/2+0.5i,- √3/2-0.5i

but the 3rd solution is incorrect, should be -i. what have i done wrong?