 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. Now 12th part is root 5 plus 3 iota Let's now start the solution Let z is equal to root 5 plus 3 iota Now we have to find the multiplicative inverse Multiplicative inverse of a non-zero complex number z is same as its reciprocate So that means we will now find 1 by z Now 1 by z is equal to 1 upon root 5 plus 3 iota right now we will multiply the numerator and denominator by conjugate of denominator that is root 5 plus 3 iota Now you should know that conjugate of a complex number a plus iota b is obtained By replacing iota with minus iota. So conjugate of a plus iota b is a minus iota b Thus conjugate of root 5 plus 3 iota is root 5 minus 3 iota right So now 1 by z is equal to 1 upon root 5 plus 3 iota into root 5 minus 3 iota upon root 5 minus 3 iota and this is equal to root 5 minus 3 iota upon In denominator, we have root 5 plus 3 iota into root 5 minus 3 iota Now this is of the form a plus b into a minus b so we can use the identity of a squared minus b squared So this expression is equal to square of root 5 minus square of 3 iota and this is equal to root 5 minus 3 iota upon 5 minus 9 iota square We know that iota square is equal to minus 1 so we have root 5 minus 3 iota upon 40 Therefore the multiplicative inverse of root 5 plus 3 iota is root 5 by 40 minus iota 3 by 40 This is our required answer. Bye and take care. Hope you have enjoyed the session