6.1 Notes.notebook
April 21, 2014
6.1 Complex Numbers
Name: __________________
Objectives: Students will be able to rewrite expressions using
complex numbers and perform operations with complex numbers.
i = _____ and
i2 = _____
Complex numbers:
Ex:
Imaginary Numbers:
Ex:
Apr 12­1:30 PM
Examples Determine whether each complex number is real or
imaginary and write it in the standard form a + bi.
1.) 3i
2.) 87
3.) 4 - 5i
4.) 0
5.) 1 + πi
2
Apr 13­7:45 AM
1
6.1 Notes.notebook
April 21, 2014
Examples Perform the indicated operations and write your answers
in standard form.
1.) (-3 + 2i) + (5 - 6i)
2.) (6 - 7i) - (3 - 4i)
3.) -3i(5 + 2i)
4.) (3 - i)(5 - 2i)
Apr 13­7:47 AM
Powers of i
i = ____
R = ____
i2 = ____
R = ____
i3 = ____
R = ____
i4 = ____
R = ____
i5 = ____
i6 = ____
i7 = ____
i8 = ____
Examples
1.) i17
2.) i98
3.) i-27
Apr 13­7:48 AM
2
6.1 Notes.notebook
April 21, 2014
Complex Conjugates:
Find the product of a + bi and its conjugate.
Examples Find the product of 4 + 3i and its conjugate.
Examples Divide and write each in standard form.
1.)
3i
-2 + i
2.) √3 - i√2
√2 + i√3
Apr 13­7:51 AM
Definition of the Square Root of Negative Number:
Examples
1.) √-16 + √-25
2.) √-3√-3
3.) (√-5)3
Apr 13­7:55 AM
3
6.1 Notes.notebook
April 21, 2014
4.) -6 + √-3
3
Examples Let T(x) = 2x2 + 1 and W(x) = x2 - 6x + 14. Find the
following:
1.) T(i√2/2)
2.) W(2 - i)
Apr 13­7:58 AM
Examples Determine whether the complex number satisfies the
`
equation following it.
1.) -4i, 2x2 + 32 = 0
2.) √2 + i√3, x2 - 2√2x + 5 = 0
Homework: Pages 311-312: Exercises: #1-4 all,
#5-89 every other odd
Apr 13­8:00 AM
4
6.1 Notes.notebook
April 21, 2014
Apr 17­11:41 AM
5