Complex number — modulus?
Distance from origin in plane.
Complex number — argument?
Angle with positive real axis.
Complex conjugate — change?
Sign of imaginary part.
Polar form — components?
Modulus and argument.
Cube roots of unity — sum?
−1.
Fourth roots of unity — product?
1.
Fourth roots of 81 — examples?
±3, ±3i.
Complex in polar — formula?
r(cosθ + i sinθ).
Function — definition?
Maps inputs to one output.
Periodic function — key property?
Repeats every T, f(x+T)=f(x).
Arithmetic progression — difference?
Constant difference between terms.
Geometric progression — ratio?
Constant ratio between terms.
Factorial — notation?
n! equals product 1 to n.
Permutation — count?
Ordered arrangements, nPr.
Combination — count?
Unordered selections, nCr.
Synthetic division — purpose?
Evaluate polynomial or divide.
Factor theorem — states?
If f(a)=0, then (x−a) is a factor.
Cos addition identity?
cos(α+β)=cosαcosβ−sinαsinβ.
Limit derivative — definition?
Limit of difference quotient as x→a.
Dot product — measures?
Alignment of vectors.
Answer 20 questions on Advanced Complex Numbers and Roots.
1. What does the modulus of a complex number represent in the complex plane?
2. What is the complex conjugate of -2 + 3i?
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