Download Complex Numbers - Math-HS

Complex Numbers
Allow us to solve equations with a
negative root
x2  2x  5  0
2   16
x
2
x
2  4  1
2
2  4i
x
2
x  (1  2i )or (1  2i )
NB: these are
complex conjugates
usually notated as z
and z
Operating on Complex Numbers in
Rectangular Form (Cartesian form)
• Multiplication
6x(3+5i)
• Addition & Subtraction
(3+2i) + (6-i)
(2-6i) – (8-4i)
• Division
(3-2i)÷(-7+3i)
30.2 p.278 #2-4
30.3 p.280 even #
30.4 even #
30.6 p.282 #4-8
The Modulus
.
.
•The modulus of a complex number represents its distance from
the origin on an Argand diagram.
•If a complex number is
, then
its modulus
Example: Evaluate
i
4
x
-2
4-2i
Example: Evaluate
if