Use the polar form of a negative real number, n, to explain why raising a negative number to odd powers results in negative value while raising a negative number to even powers result in positive values.

Step-by-step explanation:

Let r be any positive number.Then the polar form of "-r" is r(cos(180°)+isin(180°).

Then,

If n is an even integer, say n = 2k, then  

=

=

Which is a positive number.

Thus, raising a negative number to even powers result in positive values.

Now, if n is odd integer that is n=2k+1,

=

=

which is a negative number.

Thus, raising a negative number to odd powers results in negative value.

Hence proved.

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step-by-step explanation: