Complex Numeracy

Question 1

Imaginary Numbers

Answer 1

i = √-1, i² = -1

Question 2

Complex Numbers

Answer 2

• Z = |Z|²/Z = a + bi
• a, b ∈ R

Question 3

Modulus of Complex Number

Answer 3

|Z| = |a + bi| = √(a² + b²)

Question 4

Modulus Squared

Answer 4

|Z|² = Z(Z*) = a² + b² = (a + bi)(a - bi)

Question 5

Conjugate of Complex Number

Answer 5

Z* = a - bi

Question 6

Distance in a Complex Plane

Answer 6

• d = |(a - c) + (b - d)i|
• = √((a - c)² + (b - d)²)

Question 7

Symbols of distance in a complex plane

Answer 7

(a, bi) and (c, di) are points on the complex plane

Question 8

Imaginary and Real Part of a Complex Number

Answer 8

• Im(z) = b
• Re(z) = a