Angular separation on the Argand plane: What is the angular difference (in degrees) between the vectors +j4 and −j4?

Introduction / Context:
Complex numbers can be represented as vectors with angles measured from the positive real axis. Purely imaginary numbers lie on the vertical axis, making angle comparisons straightforward and important for phasor reasoning.

Given Data / Assumptions:

• +j4 lies at angle +90° (positive imaginary axis).
• −j4 lies at angle −90° (negative imaginary axis) or equivalently 270°.
• Angles measured in standard polar form.

Concept / Approach:

The angular difference between two directions is the absolute difference between their angles, wrapped to 0–180° for the smallest separation. Between +90° and −90°, the separation is 180°.

Step-by-Step Solution:

Verification / Alternative check:

Visualize the vertical axis: the two vectors point in exactly opposite directions, confirming 180° separation.

Why Other Options Are Wrong:

90° would be orthogonal, not opposite. 270° is the larger swept angle, not the minimal difference. 30° is unrelated.

Common Pitfalls:

Confusing principal angles with minimal angular separation; forgetting that −90° and 270° represent the same direction.

Final Answer:

180°