Question

How would you solve: (3 + 2i) to the power of -7 ?
This is a complex number raised to the power of -7. Would it be the inverse of the complex number raised to the + 7th power?

Answer 1

the reciprocal, yes
it is going to be a pain i would cheat

Answer 2

there is no snappy way to do this, it would take an hour of arithmetic
http://www.wolframalpha.com/input/?i=+%283+%2B+2i%29+^-7

Answer 3

Reciprocal or inverse and then raise the complex number to the positive 7th power. But to help things more, i could change the complex number to complex number to exponential form and then raise this exponential form of the complex number to the power of + 7. This would save the one hour of algebra and potential errors.

Answer 4

Convert it to polar form and use De Moivre's Theorem

Answer 5

This is the question in exponetial form: (2e to the power of -pi/6) all to the power of -7

Answer 6

This is a new question i have typed. Are complex numbers in any form,cartesian, polar or exponent form raised to a negative power the inverse of the complex number?

Answer 7

What is the inverse of a complex number? Do you mean the reciprocal?

Answer 8

yes reciprocal but our teacher using the word inverse