 Hi and welcome to the session. Let's discuss the following question. It says convert each of the complex numbers given in exercise 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 it Any complex number z is in the form x plus iota y then the modulus of z is denoted by r and it is equal to root of x square plus y square and The polar form of z is given by r into cos theta plus iota sin theta Then the argument of z is given by theta So this is the key idea Let's now move on to the solution Let the complex number root 3 plus iota Be denoted by z. So z is equal to root 3 plus iota Comparing it with x plus iota y we can see that x is equal to root 3 and y Which is equal to 1 Now we obtain the modulus which is equal to root of root 3 square plus 1 square and it is equal to root 4 and Again it is equal to 2 Now we have to obtain Argument of z that is theta for that Let us first plot the point x is equal to root 3 and y is equal to 1 on the argon plane So this is the argon plane since both the points are positive. So it lies in the first quadrant and This point is root 3 1 and its distance from the origin is 2 so this distance is Is 2 and we have to obtain the value of theta right now Z in the polar form is given by 2 into cos theta plus iota sin theta because r is 2 Also z is equal to root 3 plus iota Let's call this equation as 1 and this as 2 now since LHS of both the equations are same therefore RHS are also same So we have 2 cos theta plus iota 2 sin theta is equal to root 3 plus iota now comparing real and Imaginary part we get 2 cos theta is equal to root 3 and 2 sin theta is equal to 1 So this implies Cos theta is equal to root 3 by 2 and this implies sin theta is equal to 1 by 2 Now we have to obtain value of theta for which cos theta is root 3 by 2 and sin theta is 1 by 2 and we know that cos pi by 6 is root 3 by 2 and sin pi by 6 is equal to 1 by 2 so This implies that this theta is equal to pi by 6 That means the argument of Z is pi by 6 Hence Z in polar form is given by R that is 2 into cos pi by 6 plus iota sin pi by 6 So this is the required polar form. So this completes the question. Bye for now. Take care. Hope you enjoy the session