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1

component form

u =

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2

Linear combination

u = Pi + qJ

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3

Polar form

u = ||u||cosθi + ||u||sinθJ

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4

magnitude formula

||u|| = √(P^2 + q^2)

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5

unit vector

(P/||u||i) + (q/||u||J)

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6

Reference angle

tan-1(q/P)

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7

Dot product

u ⋅ v = (u1)(v1) + (u2)(v2)

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8

c(u ⋅ v)

cu ⋅ v or u ⋅ cv

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9

Angle between two vectors

cosθ = (u ⋅ v)/||u|| x ||v||

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10

orthogonal vector

when u ⋅ v = 0 (perpendicular)

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11

Trigonometric form

Z = a + bi

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12

Multiplication of complex numbers

Z1×Z2 = r1×r2(cos(θ1 + θ2) + i sin(θ1 + θ2))

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13

Division of complex numbers

Z1÷Z2 = r1÷r2(cos(θ1 - θ2) + sin(θ1 - θ2))

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14

Exponents of complex numbers

Z^n = r^2(cosnθ + isinnθ)

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15

root of complex numbers

u = r^(1/2)(cos(1/2)(θ +- 2πk) + isin(1/2)(θ +- 2πk))

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