Thread: Help with generalization please !

Ok i have a set of questions which asks:

• Use De moivres theorem to obtain solutions to z^n=i for n=3,4,5
• Use a graphing software to plot these roots on an Argand diagram
• generalize and prove your results for z^n=a+bi where |a+bi|=1
• What happens when |a+bi| does not equal 1

So the first 2 bullet points i can do, so i have found the roots and plotted them on the diagram. Now what the heck do they mean when they sa generalize and prove your results for a+bi=z^n?????

will appreciate any help thank you

a + bi =re^i(θ+2kπ), where r=√(a^2 + b^2), and θ is calculated using a/r = cos(θ) and b/r = sin(θ).

Your third bullet point is simply r = 1.