Question

Find the multiplicative inverse of 2+3i/3+4i

Answer 1

Step-by-step explanation:

Multiplicative inverse of 2+3i/3+4i is 3+4i/2+3i

Answer 2

The multiplicative inverse of 2+3i /3+4i is  3+4i/ 2+3i

Given:  

Complex number 2+3i/3+4i

To find:

The multiplicative inverse of 2+3i/3+4i  

Solution:

Note: When a number n is multiplied with a number n' and the result is 1  then the number n' is said to be the multiplicative inverse of n

Here, n(n') = 1

Given number is 2+3i/3+4i  

Let Z be  the multiplicative inverse of 2+3i/3+4i

Then   $Z ( \frac{(2+3i)}{(3+4i)} ) = 1$  

⇒  $Z =\frac{1}{ \frac{(2+3i)}{(3+4i)} }$  

⇒  $Z =\frac{ (3+4i)}{ {(2+3i)}{} }$  

Therefore, The multiplicative inverse of 2+3i /3+4i is  3+4i/ 2+3i

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