Mathematics | Course : Model Precalculus (Advanced Course)
Domain - The Complex Number System
Cluster - Represent complex numbers and their operations on the complex plane.
[PC.N-CN.B.5] - (+) Represent addition, subtraction, multiplication, and conjugation of complex numbers geometrically on the complex plane; use properties of this representation for computation. For example: (-1+√3i)3=8 because (-1+ √3i) has modulus 2 and argument 120°.
- Argument of a complex number
The angle describing the direction of a complex number on the complex plane. The argument is measured in radians as an angle in standard position. For a complex number in polar form r(cos θ + i sin θ), the argument is θ. - Complex number
A number that can be written as the sum or difference of a real number and an imaginary number. - Complex plane
The coordinate plane used to graph complex numbers.
[PC.N-CN.A.3] -
(+) Find the conjugate of a complex number; use conjugates to find moduli and quotients of complex numbers.
[PC.N-CN.B.4] -
(+) Represent complex numbers on the complex plane in rectangular and polar form (including real and imaginary numbers), and explain why the rectangular and polar forms of a given complex number represent the same number.
[PC.N-CN.B.6] -
(+) Calculate the distance between numbers in the complex plane as the modulus of the difference, and the midpoint of a segment as the average of the numbers at its endpoints.
[PC.F-TF.C.9] -
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.
[AQR.F-TF.C.9] -
(+) Prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve problems.