Complex Numbers

Question 1

What is the expansion of x³ -1 ?

Answer 1

(x - 1)(x² + x +1)

Question 2

What is the formula for dividing complex numbers?

Answer 2

(a + bi)/(c + di) = (ac + db)/(c² + d²) + (bc - ad/(c² + d²)

Question 3

What is the polar form of a complex number Z = x + yi ?

Answer 3

Z = r(cosθ + sinθ)
Where r = |z|= √(x)²+(y)²
θ = tan^-1(y/x)

Question 4

What is the formula for root of numbers?

Answer 4

r^1/n [cos(θ+2πk/n) + Iain(θ+2πk/n)]

Where k = 0, 1, 2, … , n-1

Question 5

What is De Moivre’s Theorem (formula for finding complex number raised by a power)

Answer 5

Z^n = r^n[cos(nθ) + isin(nθ)]