 Hi and welcome to the session. Let's discuss the following question. It says convert each of the complex number given in exercises 3 to 8 in polar form. So we have to convert this complex number into polar form and we are going to discuss the third part of the question. So let us first understand the basic approach to the problem. If we have complex number z is equal to x plus iota y then the polar form of z is equal to r cos theta plus iota r sin theta where r is the modulus given by root of x square plus y square and theta is the argument of z. So to convert a complex number into polar form we need to find theta and modulus of the complex number. So this becomes the key idea for the problem. Let's now move on to the solution z is equal to 1 minus iota. Now x is equal to 1 and y is equal to minus 1 because the real part is 1 and the imaginary part is minus 1. Now the polar form of z is r cos theta plus iota r sin theta and r is given by root of x square plus y square and it is equal to 1 square plus minus 1 square and it is equal to root 2. Now we have obtained r and to convert z into polar form we need to obtain the value of theta right. So let us first plot the point x is equal to 1 and y is equal to minus 1 on the argon plane. So this is the argon plane so we have to plot point x is equal to 1 and y is equal to minus 1 since x is positive and y is negative. So this point lies in the fourth quadrant right and its distance from origin is root 2. So we have to obtain the value of theta right. Now z is equal to 1 minus iota and in the polar form it is equal to root 2 cos theta plus iota root 2 sin theta because r is root 2. Now on comparing we get 1 is equal to root 2 cos theta and minus 1 is equal to root 2 sin theta and this implies cos theta is equal to 1 by root 2 and the second equation implies sin theta is equal to minus 1 by root 2. Now we know that cos pi by 4 is equal to 1 by root 2 and sin pi by 4 is equal to 1 by root 2 but we want to have the value of theta for which sin theta is equal to minus 1 by root 2. But the given point is in fourth quadrant so cos of minus pi by 4 is equal to 1 by root 2 and sin of minus pi by 4 is equal to minus 1 by root 2. So this implies theta is equal to minus pi by 4 and we obtained r as root 2. So z in polar form is given by root 2 cos minus pi by 4 plus iota root 2 sin minus pi by 4. Hence our answer is root 2 into cos minus pi by 4 plus iota sin minus pi by 4 by taking root 2 common we get this answer. So this completes the question. Bye for now. Take care. Hope you enjoyed the session.