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Find the multiplicative inverse of 6 + 2i.

Verified Answer :

The solution to the problem is as follows:

First thing to do is get rid of the i. Multiplying by 6 - 2i will do this 

( 6 + 2i)(6 - 2i) = 6^2 - (2i)^2 = 36 - 4(-1) = 36 + 4 = 40 

Dividing by 40 gets you 1 

(6 + 2i) (6-2i)/40 = 1 

The answer is (6 - 2i)/40 = (3 - i)/20

I hope my answer has come to your help. God bless and have a nice day ahead!

SOS

Answer:

\(\frac{3}{20}-\frac{1}{20}i\)

Step-by-step explanation:

Find the multiplicative inverse of a complex number using the process described below:

The inverse is found by reciprocating the original complex number. The reciprocal of the complex number (6+2i) is \(\frac{1}{6+2i}\). Multiply the numerator and denominator of the reciprocal by conjugate of the denominator and simplify:

\(\frac{1}{6+2i}*\frac{6-2i}{6-2i}\)

You get: \(\frac{3}{20}-\frac{1}{20}i\)

Hope this helps!!

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