Exercise 1.4

Theory (before Exercise 1.4)

Modulus

If z = a + bi then |z| = √(a² + b²)

Useful properties

• |z| ≥ 0
• |z| = 0 iff z = 0
• |z1 z2| = |z1| |z2|

Exercise 1.4 (Questions)

Q1 Compute modulus

1. z = 3 + 4i
2. z = -5 + 12i
3. z = 7 - 24i

Q2 Show

If z = a + bi, show that:

|z̄| = |z|

Q3 Mixed

Let z1 = 2 + i and z2 = 1 - 3i.

1. Find |z1| and |z2|.
2. Find |z1 z2|.
3. Verify |z1 z2| = |z1| |z2|.