 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. We have to convert this complex number in the polar form. So let us first understand the key idea to solve it. Any complex number z is in the form x plus i star y and the polar form of z is given by r into cos theta plus iota sin theta, where r is the modulus of z which is equal to root of x square plus y square and theta is the argument of z. 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. Let the complex number minus 1 plus iota be denoted by z. So z is equal to minus 1 plus iota. On comparing this with x plus iota y we can see that x is equal to minus 1 and y is equal to 1. Now to convert this complex number in the polar form we need to obtain r and theta. So let us first obtain r. r is root of x square that is minus 1 square plus y square that is 1 square which is equal to root 2. Now z in the polar form can be written as r that is root 2 into cos theta plus iota sin theta. Now we need to obtain theta. So let us first plot the point x is equal to minus 1 and y is equal to 1 on the argon plane. So let this be the argon plane and we have to plot the point x is equal to minus 1 and y is equal to 1. So this point lies in the second quadrant right. It is the point x is equal to minus 1 and y is equal to 1. Also z is equal to minus 1 plus iota. Since both these expressions are equal to z so they are equal so we have root 2 cos theta plus iota root 2 sin theta is equal to minus 1 plus 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 1. The first one implies cos theta is equal to minus 1 by root 2 and the second one implies sin theta is equal to 1 by root 2. Now we need to obtain value of theta for which cos theta is minus 1 by root 2 and sin theta is 1 by root 2 and we know that cos pi by 4 is 1 by root 2 and sin pi by 4 is 1 by root 2 but we need to have the value of theta for which cos theta is minus 1 by root 2 but this point is in second quadrant and this angle is pi. So we have cos pi minus pi by 4 is equal to minus 1 by root 2 and sin pi minus pi by 4 is equal to 1 by root 2. So this angle is 3 pi by 4 so this implies cos 3 pi by 4 is equal to minus 1 by root 2 and sin 3 pi by 4 is equal to 1 by root 2. So this implies theta is 3 pi by 4 so theta is 3 pi by 4 and hence z in polar form is given by r that is root 2 into cos 3 pi by 4 plus iota sin 3 pi by 4 which is the answer. So this completes the question. Bye for now. Take care. Hope you enjoyed the session.