EXERCISE . . Write the following in the rectangular form: (i) ( (ii) (iii) . If z iy , find the following in rectangular form.
(i) Re (ii) Re( i z (iii) Im( . If z and z , find the inverse of z z and z . The complex numbers u v , , and w are related by u v w If v and w , find u in rectangular form. .
Prove the following properties: (i) z is real if and only if z (ii) Re( ) z and Im( ) z . Find the least value of the positive integer n for which (i) real (ii) purely imaginary. . Show that (i) is purely imaginary (ii) is real.