 Hi and welcome to the 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 10 quarters minus 2 minus 1 by 3 iota whole cube. Before solving this question we 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 minus 2 minus 1 by 3 iota whole cube. We have to express this in the form a plus iota b right. We know the formula for whole cube of a plus iota b so using this formula we will express this expression in the form a plus iota b. Now here a is equal to minus 2 and b is equal to minus 1 by 3. Using this formula this expression is equal to whole cube of minus 2 minus 3 into square of minus 1 by 3 into minus 2 into minus 2 into minus 1 by 3 minus iota minus 2 is minus 8 minus 3 into square of minus 1 by 3 is 1 by 9 into minus 2 into 3 into square of minus 2 is 4 into minus 1 by 3 minus iota cube of minus 1 by 3 is minus 1 by 27. And this is equal to minus 8 cancelling 3 by 9 we get 1 by 3 so we have minus 2 by 3 plus iota we can cancel 3 from both numerator and denominator so we are left with 4 into minus 4 into minus minus minus 4 so we have iota into minus 4 plus iota upon 27 and this is equal to minus 8 plus 2 by 3 minus 4 iota plus iota upon 27. Now simplify the real part and the imaginary part this is equal to minus 22 by 3 and this is equal to minus iota 107 upon 27 so our solution is minus 22 by 3 minus iota 107 upon 27 we have expressed the given complex number in the form a plus iota b where a is equal to minus 22 by 3 and b is equal to minus 107 upon 27 this is our required answer bye and take care hope you have enjoyed the session