 Hi and welcome to this session. Let's discuss the following question. The question says express each of the complex number given in the exercises 1 to 10 in the form a plus iota b. The third part is iota raise to the power minus 39. For solving this question we will use the rules for powers of i. For any integer k, iota raise to the power 4k is equal to 1, iota raise to the power 4k plus 1 is equal to iota, iota raise to the power 4k plus 2 is equal to minus 1 and iota raise to the power 4k plus 3 is equal to minus iota. These rules will help us to solve the question. So this is the key idea in this question. Let's now start the solution. Given complex number is iota raise to the power minus 39 and this is equal to 1 upon iota raise to the power 39 and this is equal to 1 upon iota. We can write 39 as 4 into 9 plus 3. Now this is of the form iota raise to the power 4k plus 3 and this is equal to minus iota. So this expression is equal to 1 upon minus iota. We have to convert this in the form a plus iota b. So we will now multiply the numerator and denominator by iota and this is equal to iota upon minus iota square. Now iota square is equal to minus 1 and this implies minus iota square is equal to plus 1. So using this iota upon minus iota square is equal to iota. So our required answer is iota. So this completes the session. Have a good day.