Question

Find the multiplicative inverse of the following complex number Z=2+3i/2-3i​

Answer 1

Let Z

i

be the multiplicative Inverse of 2−3i

so that,

Z

i

(2−3i)=1⇒Z

i

=

2−3i

1

=

(2−3i)(2+3i)

2+3i

=

2

2

−(−3

2

)

2+3i

=

(2−3i)(2+3i)

2+3i

=

2

2

+3

2

2+3i

=

13

2

+

13