Tuesday, 3 September 2013

complex analysis - Values for (1+i)2/3



This question might seem easier than I'm making it seem. But how many values are there for (1+i)2/3? Do I let z=(1+i)2/3 so that z3=2i? I'm asked to write each in polar coordinates and in rectangular form and also sketch their location. Any help will be appreciated thank you.


Answer




Here is how you advance
z3=(1+i)2=2i=2eiπ/2=2eiπ/2ei2kπ=2eiπ/2+i2kπ



z=21/3eiπ/2+i2kπ3,k=0,1,2.


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