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Units 1: Complex Numbers and Parent Functions (Distance w/ Complex Numbers…
Units 1: Complex Numbers and Parent Functions
Distance w/ Complex Numbers
Imaginary #: y-axis
Real Numbers: x-axis
Example:
Use the Pythagorean Theorem: a^2+b^2=c^2
Video for Help
https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-distance-midpoint/v/complex-plane-distance-midpoint
Midpoint w/ Complex Numbers
Equation to Find Midpoint
x= Real Number
y= Imaginary Number
Example:
Video for Help
https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:complex/x9e81a4f98389efdf:complex-distance-midpoint/v/complex-plane-distance-midpoint
Add/Subtract Complex Numbers
Combine Like Terms
z=a+bi
Example: (-15+3i)-(5i)= -15-2i
Video for Help
Adding:
https://www.bing.com/videos/search?q=how+to+add+and+subtract+complex+numbers+khan+&&view=detail&mid=A89000A059C64CB119D7A89000A059C64CB119D7&&FORM=VRDGAR
Subtracting:
https://www.bing.com/videos/search?q=how+to+add+and+subtract+complex+numbers+khan+&&view=detail&mid=712D48BAB8DCD88E0817712D48BAB8DCD88E0817&&FORM=VRDGAR
Plotting Complex Numbers
(Rm,Im)
x= Real Numbers
y= Imaginary Numbers
Example: 3-5i
x= 3
y= -5i
Video for Help
https://www.bing.com/videos/search?q=plotting+complex+numbers&&view=detail&mid=02747BC08FC3156AFC6202747BC08FC3156AFC62&&FORM=VRDGAR
Imaginary Numbers
Represented by i
Table
There's a pattern
Unit 2: Polynomials and Piecewise Functions
Expanding Binomials
Pascals Triangle
Used in expanding to find coefficients for variables
Example
(5x-2y)^3
Steps
Figure out coefficients using Pascals Triangle
Answer:
Substitute 5x for x and -2y for y
Distribute and Solve
Video For Help
Intro to Binomial Theorem:
https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:polynomials/x9e81a4f98389efdf:binomial/v/binomial-theorem
Expanding Binomial:
https://www.khanacademy.org/math/precalculus/x9e81a4f98389efdf:polynomials/x9e81a4f98389efdf:binomial/v/coefficient-in-binomial-expansion
Limits in Graph
Defenition
An output of an input that's approaching a certain point in the graph
Vocabulary
Continuous
A smooth, unbroken curve
Discontinuity
A point in which a function is discontinuous and undefined
Removable Discontinuity
A point at which a graph is not connected
Examples
Video for Help
https://www.bing.com/videos/search?q=limits+in+graphs+khan+academy&view=detail&mid=9E0B41B72AC1A3E88FF69E0B41B72AC1A3E88FF6&FORM=VIRE
Polynomial Division/Synthetic Division
Polynomial
Synthetic
Videos for Help
Synthetic
https://www.bing.com/videos/search?q=synthetic+division+khan+academy&&view=detail&mid=B80890E8D1B39EFF9CD2B80890E8D1B39EFF9CD2&&FORM=VRDGAR
Polynomial
https://www.bing.com/videos/search?q=polynomial+long+division+khan+&&view=detail&mid=47EA6018FA2B04B83E7647EA6018FA2B04B83E76&&FORM=VRDGAR
