Complex Number
The modulus is the distance of the complex number from the origin or sqrt(a2+b2)
What is one difference between polar and cartesian planes?
*Multiple answers: radial circles around origin, rays from orgin
What transformation is induced by the following matrix:
[1 0
0 -1]
Reflects about horizontal axis
How many square roots does a complex number have?
2
Define the argument of a complex number
The argument is the angle θ formed with the positive real axis in the complex plane, measured counterclockwise.
A counterclockwise rotation of 90 degrees has the same effect as what clockwise rotation?
-90 clockwise or 270 clockwise
Multiplying by 1 in real numbers
The degree of the root or power of the complex number you are calculating
What is the polar form of a complex number with an argument of 30 degrees and modulus of 2?
2[cos(30)+i*sin(30)]
What is the transformation matrix induces by a counterclockwise rotation by pi and a dilation with a scale factor of 2?
[2*cos(pi) -2*sin(pi)
2*sin(pi) 2* cos(pi)]
[-2 0
0 -2]
What is the determinant of the matrix A?
-10
What does the k mean in the root formula?
*Accept a couple versions of wording but need to include that it has to do with how many roots or how many times the alpha formula is repeated
What is the rectangular form of z=4[cos(45)+i*sin(45)]
z=2sqrt(2)+2i*sqrt(2)
Write in the formula for the transformation of reflection z over the line y=x.
ry=x(z)=i*conj(z)
What is the inverse of Matrix A?
-1/10 -1/5
4/5 -3/5
What are the square roots of z=-5?
sqrt(5)i and -sqrt(5)i