 Hi and welcome to the session. Let's discuss the following question. It says convert each of the complex numbers given in exercises 3 to 8 in the polar form. So we have to convert this complex number in the polar form. So let us first understand the key idea to solve this problem. Any complex number z is of the form x plus iota y. Then the polar form of z is given by r into cos theta plus iota sin theta. Where r is equal to root of x square plus y square and the argument of z is theta. So to convert a complex number in the polar form we need to obtain r and theta. So this is the key idea. Let's now move on to the solution. Given complex number is minus 1 minus iota. Let's denote it by z. So z is equal to minus 1 minus iota. Comparing it with x plus iota y we can see that x is equal to minus 1 that is real part is minus 1 and imaginary part is also minus 1. Now to convert this into polar form we need to obtain r. So let us first obtain r. r is root of minus 1 square plus minus 1 square which is equal to root 2. Now to convert z in the polar form we need to obtain theta. So for that first plot the point x is equal to minus 1 and y is equal to minus 1 on the argon plane. So this is the argon plane since x is equal to minus 1 and y is equal to minus 1. So this point lies in the third quadrant and its distance from the origin is root 2 because modulus is root 2. And this point is minus 1, right? And we have to obtain the value of theta. Now z in the polar form can be written as r that is root 2 into cos theta plus iota sin theta. Also z is equal to minus 1 minus iota. Let's call this as 1 and this as 2. Now since LHS of both the equations are same therefore RHS are also same. So we have root 2 cos theta plus iota root 2 sin theta is equal to minus 1 minus iota. Now comparing real and imaginary parts we get root 2 cos theta is equal to minus 1 and root 2 sin theta is equal to minus 1. This implies that cos theta is equal to minus 1 by root 2 and this implies that sin theta is equal to minus 1 by root 2. Now we need to obtain value of theta for which cos theta is equal to minus 1 by root 2 and sin theta is equal to minus 1 by root 2. So we know that cos pi by 4 is equal to 1 by root 2 and sin pi by 4 is also equal to 1 by root 2. But we need to have value of theta for which it is equal to minus 1 by root 2. Now since this point is in third quadrant so we have cos minus pi plus pi by 4 is equal to minus 1 by root 2 and sin minus pi plus pi by 4 is equal to minus 1 by root 2. So this implies that cos minus 3 pi by 4 is equal to minus 1 by root 2 and this implies that sin minus 3 pi by 4 is equal to minus 1 by root 2. That means this angle this theta is equal to minus 3 pi by 4. So this implies theta is equal to minus 3 pi by 4. Hence z in polar form can be written as r that is root 2 into cos minus 3 pi by 4 plus iota sin minus 3 pi by 4 which is the required polar form. So this completes the question. Bye for now. Take care. Hope you enjoyed this session.