SOLUTION: find the Cartesian form of x+iy of the complex numbers (1+i)^-5

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Question 1181959: find the Cartesian form of x+iy of the complex numbers
(1+i)^-5
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.
find the Cartesian form of x+iy of the complex numbers
(1+i)^-5
~~~~~~~~~~~~~~~ 

%281%2Bi%29%5E%28-5%29 = %28sqrt%282%29%2Acis%2845%5Eo%29%29%5E%28-5%29 = %281%2F%284%2Asqrt%282%29%29%29%2Acis%28%28-5%29%2A45%5Eo%29 = %281%2F%284%2Asqrt%282%29%29%29%2Acis%28-225%5Eo%29 = %281%2F%284%2Asqrt%282%29%29%29%2Acis%28135%5Eo%29 = -%281%2F8%29+%2B+i%2A%281%2F8%29%29.       ANSWER

Solved.



Answer by greenestamps(13203) About Me  (Show Source):
You can put this solution on YOUR website!


Put the given number (1+i) in AcisB form and use deMoivre's Theorem to perform the operations of division and raising to a power.

%281%2Bi%29=%28sqrt%282%29%29cis%2845%29





Then convert the answer back to a+bi form.



ANSWER: %28-1%2F8%29%2B%281%2F8%29i