20 CHAPTER l • COMPLEX N UMBERS
yFigure 1.10 The geometry of mul t iplicat ion.
-------~EXERCIS ES FOR SECTION 1. 3
- Evaluate the following quantities. Be sure to show your work.
(a) 1 (1 + i) (2 + i)I.
(b) I ~-:.~i I·
(c) l(l + i)6ol ·
(d) Izzi, where z = x + iy.
(e) lz - 112 , where z = x + iy.- Locate z1 and z2 vectorially and use vectors to find z1 + Z2 and z 1 - z2 when
(a) z1 = 2 + 3i and z2 = 4 + i.
(b) z1 = - 1 +2i and z2 = -2+3i.
(c) z1 = 1 + iv'3 and z2 = - 1 + i\1'3.- Which of the following points lie inside the circle lz -ii = 2? Explain your answers.
(a)! +i.
(b) v'2 + i( v'2 + 1).
(c) 2 + 3i.
( d) ·:} + iv'3.4. Prove the following Identities.(a) (1- 21).
(b) (1-22).
(c) (1-26).- Show that the no02ero vectors z1 and z2 are perpendicular iff Re(z1z2) = O.