 Welcome to the session. I am Arsha and I am going to help you with the following problem which says convert the following in polar form. We have to convert 1 plus 3 iota upon 1 minus 2 iota. So let us begin with the solution and let x plus iota y be equal to 1 plus 3 iota upon 1 minus 2 iota. Now to reduce it in the form of x plus iota y, let us rationalize it. So, multiplying the numerator and denominator by the conjugate of 1 minus 2 iota by just 1 plus 2 iota. So it can further be written as 1 plus 3 iota into 1 plus 2 iota and the denominator 1 square minus 2 iota whole square which is further equal to 1 plus 3 iota plus 2 iota minus 6 upon 5. So we have minus 5 plus 5 iota upon 5. Now taking 5 common and canceling the common multiple we have minus 1 plus iota which is equal to x plus iota y and now I am comparing we find here that x is equal to minus 1 and y is equal to 1. Now any complex number z the standard form x plus iota y in polar form can be written as r into cos theta plus iota sin theta where r is root over x square plus y square and theta is the argument of z. So first let us find the value of r which is root over x square plus y square and x is minus 1 whole square y is 1. So we have root over 2 as the value of r. So z which is equal to x plus iota y is further equal to r cos theta plus iota sin theta 10 before the written as x plus iota y is equal to root over 2 cos theta plus iota sin theta where x is minus 1 plus y is 1. So we have minus 1 plus iota is equal to root over 2 cos theta plus root over 2 sin theta iota. Now on comparing the real and imaginary parts we find minus 1 is equal to root over 2 cos theta and 1 is equal to root over 2 sin theta which further implies that cos theta is equal to minus 1 upon root 2 and sin theta is equal to 1 upon root 2 and now we need to find the value of theta. Now cos theta is equal to minus 1 upon root 2 and sin theta is equal to 1 upon root 2 implies that theta is equal to 3 pi upon 4 and so our answer the polar form s r which is root over 2 cos theta it has 3 pi by 4 plus iota sin 3 pi by 4. So this is the polar form of the given expression which completes the solution hope you enjoyed it take care and have a good day