Reading the Argand plane: The point labelled +4 on the complex plane represents which position relative to the origin?

Introduction / Context:The Argand (complex) plane is a visual tool for representing complex numbers where the horizontal axis is the real part and the vertical axis is the imaginary part (often denoted by j in electrical engineering). Understanding this mapping is useful for visualizing phasors, impedances, and frequency responses.

Given Data / Assumptions:

• The label +4 without a j indicates a purely real number: 4 + j0.
• Standard axes: real axis horizontal, imaginary axis vertical.

Concept / Approach:A purely real number positions entirely along the real axis. A positive real value lies to the right of the origin, while a negative real value lies to the left. Imaginary values would place the point along the vertical axis instead.

Step-by-Step Solution:

Verification / Alternative check:Polar representation: magnitude = 4, angle = 0°. An angle of 0° aligns with the positive real axis, confirming location to the right of the origin.

Why Other Options Are Wrong:

• Left on the real axis: would correspond to −4.
• Above or below on the j axis: would require a nonzero imaginary part (±j4).

Common Pitfalls:

• Confusing the j axis as horizontal; by convention it is vertical in engineering contexts.

Final Answer:4 units right of the origin on the real axis