 Hi, and welcome to the session. Let's discuss the following question. The question says express the following expression in the form of a plus iota b. Given expression is 3 plus iota root 5 into 3 minus iota root 5 upon root 3 plus root 2 iota minus root 3 minus iota root 2. Let's now start the solution. We have to express the expression 3 plus iota root 5 into 3 minus iota root 5 upon root 3 plus root 2 iota minus root 3 minus iota root 2 iota form a plus iota b. Vumerator is 3 plus iota root 5 into 3 minus iota root 5. So we can use the identity of a square minus b square. So using this identity, numerator is equal to square of 3 minus square of iota root 5. In denominator, we have to find the difference of two complex numbers. So we will now apply the rule for difference of two complex numbers. That means we will take the real and imaginary parts in separate packets. So denominator is equal to root 3 minus root 3 plus root 2 square of 3 is 9 and square of iota root 5 is 5 iota square. root 3 minus root 3 is 0 plus iota root 2 plus root 2 is 2 root 2. We know that iota square is equal to minus 1. So numerator is equal to 40 and denominator is equal to 2 root 2 iota. We want the answer in the form of a plus iota b. So we will now remove root 2 iota from the denominator. So multiply the numerator and denominator by minus root 2 iota is equal to minus 14 root 2 iota upon minus 4 iota square and this is equal to minus 14 root 2 iota upon 4 and this is equal to minus 7 root 2 iota upon 2. So our required answer is minus 2 iota upon 2. This completes the session. Bye and take care.