Download 7.7 Geometric Application - Onondaga Community College

6.7 Geometric Application
6.8 Complex Numbers
Pythagorean Theorem
• c2 = a2 + b2
Hypotenuse c
a2
b2
So c = +
• a = c2 - b2
• b = c2 - a2
Leg a
Leg b
Examples
c=?
a=3
b=5
c=13
b=12
a=?
Examples
1) A square has the
diagonal of 3 2.
Find the side of the square
3 2
2) Find c
c=?
4cm
Examples using Pythagorean
Theorems
2) The base of a 10 ft long guy wire is
located 7 ft from the telephone pole. How
high is the pole?
6.8 Complex Numbers
Draw set of complex numbers
An imaginary number is a number that can be
written as:
a + bi (a, b Є R, b ≠ 0)
Example: -3 + 4i, or 8i
i   1  i  1
2
 16   116  4  1  4i
  20    1  4  5  2 5i or  2i 5
 5  5i
Complex number a + bi (a, b Є R, a, b can be 0)
Complex numbers: include real and imaginary #s
Example:
-3 + 4i
8i
-5
3
2
Power of i:
i  1
i  1
2
i  i  i   1  i
3
2
i  (i )  (1)  1
4
2 2
i  i
5
2
  i  1 (i)  i
2 2
i  (i )  (1)  1
6
2 3
3
Even power -1 or 1; Odd power –i or i
i
24
 i
  1
2 12
12
1
i12 =
1
i30 =
-1
i17 =
i
i43 =
-i