I need to find the rectangular form of i ^ (-3) + i ^ (-2)

i = imaginary number

The answer in my book says -1 + i but i do not know how they got it

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- Jan 16th 2008, 09:35 PMOzzManComplex Numbers
I need to find the rectangular form of i ^ (-3) + i ^ (-2)

i = imaginary number

The answer in my book says -1 + i but i do not know how they got it - Jan 16th 2008, 09:40 PMmr fantastic
$\displaystyle i^{-3} = \frac{1}{i^3} = \frac{1}{i \times i \times i} = \frac{1}{-i}$

Multiply top and bottom by i:

$\displaystyle = \frac{i}{-i \times i} = \frac{i}{1} = i$.

$\displaystyle i^{-2} = \frac{1}{i^2} = \frac{1}{i \times i} = \frac{1}{-1} = -1$.

Therefore ...... - Jan 16th 2008, 09:43 PMearboth
- Jan 16th 2008, 10:37 PMOzzMan
why do you multiply top and bottom by i ?

- Jan 16th 2008, 11:03 PMOzzMan
oh is it because the conjugate of -i is i?

- Jan 16th 2008, 11:14 PMmr fantasticQuote:

Originally Posted by**mr fantastic**

*you*do .....?

Returning to

Well, yes it is. But it also happens to be the easiest way to express $\displaystyle \frac{1}{-i}$ in rectangular form .....