The discussion revolves around evaluating the expression (3/(1-i)-(1-i)/2)^40, which involves complex numbers. Participants are exploring the simplification and computation of this expression, particularly using polar form and de Moivre's theorem.
Some participants have confirmed similar results, while others express uncertainty about the accuracy of their computations. There is a suggestion that the problem may have been copied incorrectly, which could affect the approach taken. The discussion is ongoing with various interpretations being explored.
Participants mention the complexity of calculations by hand and the potential for errors in the problem statement itself, which may impact their approaches and results.
I get this (above) also.iamavisitor said:Homework Statement
Please help me find (3/(1-i)-(1-i)/2)^40. I got a result (see below) but I'm not sure whether it is correct. Any help is appreciated. Thanks.
Homework Equations
The Attempt at a Solution
I got (1+2i)^40.
The way to go here is to convert 1 + 2i into polar form, using the Theorem of de Moivre. Then raising to the 40th power is easy.iamavisitor said:After this I got some funny numbers like 7^10*16*(6232-474*i).
No, it's not complicated to do by hand once you have the complex number in this form.iamavisitor said:I know about de Moivre's formula. With it I get radius (r) to be sqrt(5) and angle 63.43 degrees. Again this is complicated to do by hand and I am wandering whether I got something wrong.