 Hello and welcome to the session. In this session we will discuss a question which says that using d-nivus theorem, find the value of 1 by root 2 plus iota 1 to 1 by root 2 over s to power 5 plus 1 by root 2 minus iota 1 to 1 by root 2 over s to power 5. Now before starting the solution of this question, we should know our result. And that is the d-nivus theorem. According to this, if n is any integer positive or negative, then cos theta plus iota sine theta over s to power n is equal to n theta with theta. n is any fraction positive or negative theta sine theta over s to power n is equal to cos n theta theta sine n theta. That will work out as a key idea. For solving this, and now we will start with the solution. Now using the d-nivus theorem, we have to find the value of this. So there we have to find the value of 1 by root 2 plus iota root to 1 by root 2 over s to power 5 iota into 1 by root 2 over s to power 5. Now let into 1 by root 2 is equal to r into cos theta sine theta the whole. Now comparing the real and imaginary parts, this implies cos theta. Now let us name it as 1. Now squaring plus 1 by root 2 whole square is equal to cos square theta plus 1 by 2 is equal to taking r square common, it will be r square into square theta. Further, this implies 1 is equal to r square into cos square theta plus sine square theta is 1 by 2 1 which further gives. Now dividing we here prime theta r cos theta is equal to 1 by root of theta is tan theta is equal to now tan pi by 4 is 1 so it will be tan pi by 4 which implies theta is equal to pi by 4. Now let us name into 1 and now put in the values theta into 1 by root 2 is equal to which is 1 into cos pi by 4 theta which will be sine root 2 is equal to 1 into these values this will be 1 raise to the power 5 into super phi plus 1 which is given in the key idea so this will be equal to 1 raise to the power 5 which is 1 sine theta root s to power n will be cos and theta which will be cos which will be a u star sine, sine theta root s to power n will be, which will be cos and theta which will be a u star sine and this will be into cos is equal to 2 into theta is equal to minus cos theta. So this will be into cos pi by 4. And this is equal to minus 2 into cos 1 by root 2. This will be equal to minus 2 on solving. This is equal to minus root portion of the given question. And that's all for this session. Hope you all have enjoyed this session.