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Common Core Standard: HSN-CN.A.3
Multiplying Complex Numbers| Patterns of i
Week 4 Standard: Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers (CCSS.Math.Content.HSN-CN.A.3).
The Math standard covered this week is: "The student will perform operations on complex numbers, express the results in simplest form, using patterns of the powers of i, and identify field properties that are valid for the complex numbers. "
Common Core Math Standard
Key point # 1
When dividing by i, multiply the numerator and the denominator by the conjugate of the denominator.
A conjugate sounds fancy, but it is just changing the sign of two terms.
Examples:
2+4i the conjugate equals 2-4i
3+6i the conjugate equals 3-6i
a+b the conjugate equals a-b
Key point #2:
When finding the area of a rectangle, with polynomial expressions, just multiply the polynomials.
When finding the area of a triangle with polynomial expressions you multiply ½ times the base and height.
- 0:20 (-4)^i After multiplying the complex numbers you then use the patterns of i.
- 0:35 When solving this problem you multiply two complex numbers together.
- (9-7i)(-6-5i)
- Also, with this problem when you multiply the polynomial you foil the problem.
- 1:47 This problem involves dividing the complex numbers 4+i/5^i
- Remember you can have -i which is a radical in the denominator,therefore you get of i by multiplying by -i
- 3:30 This problem involves a full complex number and you have to multiply by a conjugate.
Quick review of the patterns of i and then several example problems.
Video Guide
- 0:08 Review of the patterns of i
- 0:47 Simplify i^103
- Divide 103 by four in order to use the patterns of i
- 1:26 Simplify 5i times the square root of 64
- Remove the number from the radical then simplify and use the patterns of i
- 2:17 Simplify Square root of -9 x square root of -36
- 3:05 Adding and combining complex numbers
- 2+(-8+13i)-9
- 3:40 Another problem adding and combining complex numbers.
- (-2+6i)-(5+3i)
Example problems involving adding,subtracting and multiplying polynomials.
Video Guide
- 0:27 Adding polynomials.
- 0:47 Subtracting polynomials. Remember,with subtraction you have to distribute the negative exponent to all of the terms.
- 1:31 Solves (x-4)^2 You write these out and then FOIL
- 2:23 Finding the area of a rectangle given polynomial expressions for the rectangle sides. This actually involves just multiplying the polynomials. In order to multiply the polynomials you FOIL the problem.
- 3:06 Finding the area of a triangle with polynomial expressions. This problem involves multiplying 1/2 times the measurements.