ALGEBRA 2
5.5: Complex Numbers & Roots
Imaginary Numbers
• Invented to solve quadratics that have no zeros
• What happens when we have the square root of a negative
– i
–
1
i  1
2
1) 4
2) 32
5)2i 3i
3)  25
6) 2 32
4)2 24
Solve Simple Quadratics with Imaginary
Numbers
1) x2 = -144
2) 5x2 + 90 = 0
Complex Numbers
• a + bi
– a is the real part
– b is the imaginary part
•
•
•
•
When b = 0, _____________
When a = 0, _____________
a+bi = c+di, when a =c and b=d
Computations with complex #’s
– Treat i just like a variable
– Remember i2 = -1
Examples
1) (4 + 3i) + (7 + 8i)
2) (4 + 2i) (3 – 5i)
3) Find the values of x and y that make the
equation 4x + 10i = 2 – (4y)i true.
Find complex zeros using complete the square.
1) f(x) = x2 + 10x + 26
2) g(x) = 3x2 + 12x + 36
Complex Conjugates
• Real parts are the same and the imaginary parts are
opposites
• (a + bi) & (a – bi)
• This is what occurs when the roots are complex
(previous slide)
• Example: Find each complex conjugate
1) 8 + 5i
2) 6i
Assignment #5
• Page 353 #’s 18-36,(96)