Download 5.7.2 * Complex Numbers

5.7.2 – Complex Numbers
• From yesterday, we learned the application of the imaginary unit i
• Used for problems such as;
• -5x2 = 20
Complex Number
• As part of the imaginary numbers and the imaginary number system,
we have what are known as Complex Numbers
• What does the word complex mean?
• a + bi
• a = real number
• bi = imaginary number
Combining Complex Numbers
• Similar to like variables (2x, 10x, -x) and like powers (x4, 10x4), we may
combine line terms from complex numbers
• To add or subtract complex numbers, we do the following
• 1) Combine the real parts with real parts
• 2) Combine the imaginary parts with imaginary parts
• Example. Simplify the following expressions
• 1) (2 + 5i) + (3 + 10i)
• 2) (-9 – 4i) + 10i
• 3) -13i – (4 + 6i)
• 4) 19i – 5i + 2
Multiplication
• With multiplication, we will treat them as a previous problem we
have already done
• What does the problem (2 + 5i)(1 + i) resemble?
• Is there a previous method we can use to help us?
• May use “FOIL” or the punnett square method
• Example. Find the product of the two complex numbers; (2 + 5i)(1 + i)
• Example. Find the product of the two complex numbers;
• (3 - 2i)(3 + 2i)
• Example. Find the product of the two complex numbers;
• (-4 - i)(-4 + 4i)
• Example. Find the product of the two complex numbers;
• (i + 3)2
• Complete the following problems with your neighbors. We will check
answers in 5 minutes.
• Simplify each of the following expressions.
• 1) 2 + 4i + 17 – 6i
• 2) (9 + 7i) – (4 – 5i)
• 3) (2 + i)(7 – 3i)
• 4) (6 + 2i)(1 + 2i)
• Assignment
• Pg. 265
• 27 – 49 odd