 Hi, and welcome to this session. I'm Kanika, and I'm going to help you to solve the following question. The question says, find the multiplicative inverse of each of the complex numbers given in the exercises 11 to 30. 11 car tests, 4 minus 3 iota. Let's now proceed on with our solution. When Z is equal to 4 minus 3 iota, we have to find the multiplicative inverse of 4 minus 3 iota. A multiplicative inverse of a non-zero complex number Z is same as its reciprocal. So that means we have to find 1 by Z. Now 1 by Z is equal to 1 upon 4 minus 3 iota. Right, now we will multiply the numerator and the denominator by conjugate of denominator that is 4 minus 3 iota. Now you should note that conjugate of a complex number A plus iota B is obtained by replacing iota by minus iota. So conjugate of A plus iota B is A minus iota B. Right, so conjugate of 4 minus 3 iota is 4 plus 3 iota. So now 1 by Z is equal to 1 upon 4 minus 3 iota into 4 plus 3 iota upon 4 plus 3 iota. This is equal to 4 plus 3 iota. Now in denominator we have 4 minus 3 iota into 4 plus 3 iota. We can now use the identity of A square minus B square. Right, so this is equal to 4 square minus square of 3 iota and this is equal to 4 plus 3 iota upon 16 minus 9 iota square. You know that iota square is equal to minus 1. So this is equal to 4 plus 3 iota upon 25. Therefore the multiplicative inverse of 4 minus 3 iota is 4 upon 25 plus iota 3 by 25. This is our required answer. Bye and take care. Hope you have enjoyed the session.