 Hi and welcome to this session. I'm Kanika and I'm going to help you to solve 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. Ninth part is whole cube of 1 by 3 plus 3 iota. Before solving this question you should know that whole cube of a plus iota b is equal to a cube minus 3 b square a plus iota 3 a square b minus iota b cube. This is the key idea in this question. Proceed on with our solution. Given complex number is whole cube of 1 by 3 plus 3 iota. Right. We know the formula of whole cube of a plus iota b. Now here a is equal to 1 by 3 and b is equal to 3. Now using this formula this expression is equal to 1 by 3 whole cube minus 3 into 3 square into 1 by 3 plus iota into 3 into square of 1 by 3 into 3 minus iota into cube of 3. And this is equal to 1 by 27 minus 3 into 9 into 1 by 3 plus iota into 3 into 1 by 9 into 3 minus iota into 27. And this is equal to 1 by 27. We can cancel 3 from both numerator and denominator. So we are left with minus 9 plus 3 into 3 is 9. So we have 9 by 9. 9 by 9 is 1. So we are left with only iota minus 27 iota. And this is equal to. Now solve the real part and imaginary part separately. 1 by 27 minus 9 is equal to minus 242 upon 27 iota minus iota 27 is equal to minus 26 iota. Hence our required solution is minus 242 upon 27 minus 26 iota. So we have expressed the given complex number in the form a plus iota b where a is equal to minus 242 by 27 and b is equal to minus 26. This is our required answer. Bye and take care. Hope you have enjoyed the session.