Exam-Style Problem
⬅ Back to Subchapter
Browsing as Guest. Progress, bookmarks and attempts are disabled.
Log in to track your work.
June 2013 p33 q7
1991
The complex number z is defined by z = a + ib, where a and b are real. The complex conjugate of z is denoted by z*.
- Show that |z|2 = zz* and that (z - ki)* = z* + ki, where k is real.
\(In an Argand diagram a set of points representing complex numbers z is defined by the equation |z - 10i| = 2|z - 4i|.\)
- Show, by squaring both sides, that zz* - 2iz* + 2iz - 12 = 0. Hence show that |z - 2i| = 4.
- Describe the set of points geometrically.
Log in to record attempts.