Multiplicative Inverse

Date: 6/2/96 at 10:56:30
From: Anonymous
Subject: Multiplicative Inverse

Find the multiplicative inverse of 2+5i.

Date: 6/2/96 at 16:53:25
From: Doctor Anthony
Subject: Re: Multiplicative Inverse

We require (2+5i)(a+ib) = 1
                  a+ib  = 1/(2+5i) 

Multiply top and bottom by the conjugate of (2+5i), that is (2-5i)

                       = (2-5i)/{(2+5i)(2-5i)}
                       = (2-5i)/(4+25)
                       = (2-5i)/29
                       = 2/29 - (5/29)i 

-Doctor Anthony,  The Math Forum
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