Explanation

The modulus is the distance from the origin.

For z = a + bi:
|z| = √(a² + b²)

The argument (arg z) is the angle the complex number makes with the positive real axis.

arg(z) = θ = tan⁻¹(b / a)

Quiz

1. What does |z| represent?

2. Find |3 + 4i|.

3. What does the argument measure?

4. Which trig function finds the argument?

5. Is the argument an angle?

Answer Key

1. Distance from origin

2. 5

3. Angle from the real axis

4. Inverse tangent

5. Yes