Unit 1: Test 2

Complex Number

100

What is the modulus of a complex number? 

The modulus is the distance of the complex number from the origin or sqrt(a²+b²)

200

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.

300

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)]

400

What is the rectangular form of z=4[cos(45)+i*sin(45)]

z=2sqrt(2)+2i*sqrt(2)

Transformations

100

What is one difference between polar and cartesian planes? 

*Multiple answers: radial circles around origin, rays from orgin 

200

A counterclockwise rotation of 90 degrees has the same effect as what clockwise rotation? 

-90 clockwise or 270 clockwise

300

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]

400

Write in the formula for the transformation of reflection z over the line y=x.

r_y=x(z)=i*conj(z) 

Matrices

100

What transformation is induced by the following matrix: 

[1        0

0          -1]

Reflects about horizontal axis

200

What effect does multiplying by the identity matrix have?

Multiplying by 1 in real numbers

300

What is the determinant of the matrix A? 

-10

400

What is the inverse of Matrix A? 

-1/10        -1/5

4/5           -3/5

Roots & Exponents

100

How many square roots does a complex number have?

2

200

What does the "n" represent in the exponent and root formulas? 

The degree of the root or power of the complex number you are calculating 

300

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

400

What are the square roots of z=-5?

sqrt(5)i and -sqrt(5)i