 Hi, and welcome to our session. Let's discuss the following question. The question says, it's with each of the complex numbers given in exercises 1 to 10 in the form A plus iota B. Second part is, iota raised to the power 9 plus iota raised to the power 90. For solving this question, we will use the rules for powers of i. For any integer k, iota raised to the power 4k is equal to 1. iota raised to the power 4k plus 1 is equal to iota. iota raised to the power 4k plus 2 is equal to minus 1. iota raised to the power 4k plus 3 is equal to minus iota. With the help of these rules, we will solve this question. So this is the key idea in this question. Now, we can get the solution. Given complex number is iota raised to the power 9 plus iota raised to the power 90, we have to express this in the form A plus iota B. We can write iota raised to the power 9 as iota raised to the power 4 into 2 plus 1. And we can write iota raised to the power 19 as iota raised to the power 4 into 4 plus 3. iota raised to the power 4 into 2 plus 1 is of the form iota raised to the power 4k plus 1. So this clearly implies that iota raised to the power 9 is equal to iota plus iota raised to the path 4 into 4 plus 3 is of the form iota raised to the path 4k plus 3. So this nearly implies iota raised to the path 19 is minus iota and this is equal to 0. Now 0 can be written as 0 plus iota 0 this is clearly in the form a plus iota b hence the required answer is 0. This completes the session. Bye and take care.