 Hello and welcome to the session. In this session we will discuss a question which says that if minus root 2 plus iota whole raise to power 13 is equal to 2 raise to power 13 into a plus iota b the whole, then show that the ordered pair AB is equal to the ordered pair minus root 3 by 2, 1 by 2. Now before starting the solution of this question we should know our result and that is D minus theorem. According to this if n has any integer positive or negative then plus iota sine theta whole raise to power n is equal to cos n theta plus iota sine n theta. Now this result will work out as a key idea for solving out this question. We will start with the solution. In the question this is given to us, so given minus root 3 plus iota whole raise to power 13 is equal to 2 raise to power 13 into a plus iota b the whole. Now minus root 3 plus iota the whole can be written as 2 into minus root 3 by 2 plus 1 by 2 into iota the whole which is further equal to, now minus cos pi by 6 is minus root 3 by 2 is 1 by 2. So this can be written as pi by 6 plus iota sine other 6 the whole can be written as 2 into iota 3 raise to power 13 can be written as the whole raise to power 13. Now this is equal to 2 raise to power 13 into 150 degrees the whole raise now using this result which is given as the key idea. So this will be equal to 2 raise to power 13 into 230 and theta has 150 degrees. So cos n theta will be cos 13 into 150 degrees which will be equal to powers 1,950 degrees plus iota which will be again 13 into 150 degrees which will be sine equal to 950 degrees. The whole is equal to cos 150 degrees and 50 degrees is equal to sine 150 degrees. So this will be iota 13 into cos 150 degrees plus iota sine 150 degrees the whole. So this is equal to 2 raise to power 13 further this is equal to 2 raise to power 13 into now cos 30 degrees is root 3 by 2 so it will be minus root 3 by 2 sine 30 degrees is 1 by 2 so it will be iota into 1 by 2 the whole. iota whole raise to power 13 is equal to 2 raise to power 13 into minus root 3 by 2 plus iota into 1 by 2 the whole. It is given that minus root 3 plus iota whole raise to power 13 is equal to 2 raise to power 13 iota be the whole. Theta is 1 and this is comparing 1 will be equal to minus root 3 by 2 b will be equal to 1 by 2 hence the a b is equal to the ordered pair minus root 3 by 2 1 by 2. So this is the solution of the given question and that's all for the session hope you have enjoyed the session.