Reciprocal of a complex number

I am asked to solve this

I looked over the book to see how this is done...

*according to the book*

* is to be written in stnrd form a+bi, so then one must multiply both the denominator and numerator by the opposite of the denominator in this case **3-4i*.

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Ok here is where I don't get it, what happened(s) to the and the signs in the denominator of

is the multiplication process of the denominator the same as using foil?! or am I just full of complex numbers!?

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Where did the 25 come from?!

Thanks in advance to all!!

(Handshake)