5.4 Imaginary Numbers
Warm Up
Solve the following equations :
1.) 2( x − 1) 2 = −40
2.) 5 x 2 − 15 = −5
Quadratic Equations with no real solution use an imaginary unit to represent
their answers.
Imaginary unit __________ =____________
1.) i =
2.) i 2 =
3.) i 3 =
4.) i 4 =
5.) i 5 =
Using the information you learned above decide whether the power of i is equal
to 1, − 1, i, or − i.
1.) i 9 =
3.) i 22 =
2.) i 40 =
4.) i 100 =
5.4 Imaginary Numbers
For the below equations solve the equation, simplify the radical, and write the
answer in terms of i if necessary.
1.) x 2 + 64 = 0
2.) x 2 + 1 = 0
Check:
Check:
3.) 3 x 2 + 10 x = −26
4.) 2 x 2 + 26 = −10
1
5.) − ( x + 1) 2 = 5
2
6.) − 6( x + 5) 2 = 120
5.4 Imaginary Numbers
GRAPHING
Standard form of an imaginary number is: ______________________
Graph:
1.) -2+3i
2.) 4i
3.) 1-5i
imaginary
real
Absolute Value and Complex Numbers:
The absolute value of a complex number denotes how far away the complex
number is from the origin.
If z = a + bi , the absolute value of z is defined as: ___________________
Plot the following numbers in a complex plane. Then find the absolute value of
each complex number to determine which number is the furthest from the origin.
1.) 3 + 4i
2.) -2i
3.) -1+5i
real
imaginary
Homework: Pg. 277-279 #17-36, 65-71 odd
5.4 Imaginary Numbers