Flashcard: Advanced Complex Numbers and Roots — 20 carte

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.