2. The Imaginary Unit
Not all quadratics have real number
solutions.
Example: x2 = -1 has no real solution. (A
number squared can’t be negative.)
Imaginary units are numbers that can
be represented by equations but could
not physically exist in real life.
3. Since , i can be used to write
the square root of any negative
number.
If r is a positive real #, then
◦ Example:
It follows that
◦ Example:
6. Complex Numbers
In standard form, a complex number is
a number a + bi where a and b are real
numbers.
a is the real part.
bi is the imaginary part.
If b 0, a + bi is an imaginary number.
If a = 0 and b 0, a + bi is a pure
imaginary number
7. Examples
Real numbers (a + 0i):
◦ -1, 5/2, 3,
Imaginary Numbers (a + bi , b 0):
◦ 2 + 3i, 5 – 5i
Pure Imaginary Numbers (0 + bi, b 0):
◦ -4i, 6i
8. Plotting Complex Numbers
Plotted on the complex plane.
Horizontal axis = real axis
Vertical axis = imaginary axis
imaginary
Plot:
2 – 3i
-3 + 2i real
4i