x - Balliol College - University of Oxford

SJ Roberts - July 2011 Revision 1/ page 8
5 Complex Algebra
Complex Algebra is no longer in the "Common Core" at A-level, though
some courses contain it. Whether you are familiar with it or not, you can
read about it in Chapter 7 of Stephenson --- or indeed in many A-level
texts. We will use the notation that a complex number z x
iy
,
where x is the Real part of z, y is the Imaginary part of z, and i is the
Imaginary unit such that 1
2
i . That is, x Rez
and y Imz
electrical engineering j is used instead of i to avoid confusion with the
symbol for electric current.
. In
31. Evaluate (i) (1+2i) + (2+3i); (ii) (1+2i)(2+3i); (iii) 3
1 2i
and plot the
resulting complex numbers on an Argand diagram (shown above).
32. If z x
iy , its complex conjugate is defined as z x
iy
2 2
Show that zz
x
y
.
.
33. By multiplying top and bottom of the complex fraction by the
1
2i
complex conjugate of (3+4i), evaluate .
3 4i