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Calculus/Complex numbers

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Expert: - 3/1/2009


Question
(i)Find the modulus & argument of each of the complex numbers z= (1+i)/(1-i) & w=(2^.5)/(1-i).(ii)hence show that tan((3pi)/8)=2^.5+1. I dont know how to do part 2,can you guide me? Part 1 ,i know how to do but if possible, can you give me the final answers only for part 1. Hehe,i want to check if my answers ,correct or not. Much appreciated

Answer
For both variables, multiply by the conjugate of the denominator.
That is, multiply the numerator and denominator of both fractions
by (1+i).  In the base this will give you a (1-iČ), which is 2.

I'm not sure where this relates to the tan(3pi/8) since the angle
between them appears to be pi/4.  

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