Chapter 6 Main Ideas

Head Minus Tail (HMT) Rule

Magnitude of a Vector

|v| = √a²+b² or

Vector Addition

Add the x values and then add the y values

Scalar Multiplication

Multiply each component of the vector by the number

Unit Vectors

Resolving Vectors into their Components

Dot Product of Vectors

Multiply the x values by the y values and add them together

ex: u = <u₁, u₂> & v = <v₁, v₂> so u⋅v = u₁v₁ + u₂v₂

Projectile Motion with Parametric Curves

The graph of (x, y) is defined where x = f(t) and y = g(t). T is the parameter and there will be a parameter interval.

Finding all Polar Coordinates of a Point

Coordinate Conversion X Equation

Coordinate Conversion Y Equation

Coordinate Conversion R Equation

Coordinate Conversion θ Equation

Rose Curve Properties

The graphs are given by the general equations r = acosnθ and r = asinnθ where n is an integer greater than 1. If n is odd then there are n petals and if n is even there are 2n petals

Absolute Value (Modulus) of a Complex Number

Trigonometric(Polar) Form of a Complex Number

Product of Complex Numbers

Quotient of Complex Numbers

De Moivre’s Theorem

Finding nth Roots of a Complex Number