Complex plane location: In the Argand diagram (complex plane), the complex number 4 + j3 lies in which quadrant?

Introduction / Context:
Complex numbers are fundamental to AC circuit analysis, where impedances and phasors are represented as points or vectors on the complex (Argand) plane. The sign of the real and imaginary parts determines the quadrant, which in turn indicates the phase relationship and the nature of reactive elements in circuits.

Given Data / Assumptions:

• Complex number: 4 + j3.
• Real part (Re) = 4; Imaginary part (Im) = +3.
• Standard quadrant convention: Re on x-axis, Im on y-axis; positive directions are to the right and upward.

Concept / Approach:
Quadrants are defined by the signs of (Re, Im): QI (+,+), QII (−,+), QIII (−,−), QIV (+,−). Simply check the signs of the real and imaginary components to place the number appropriately on the Argand plane.

Step-by-Step Solution:

Verification / Alternative check:
Polar form check: magnitude = √(4^2 + 3^2) = 5, angle = arctan(3/4) ≈ 36.87°, which lies between 0° and 90°, confirming Quadrant I.

Why Other Options Are Wrong:

• Second quadrant: would require a negative real part.
• Third quadrant: both parts negative.
• Fourth quadrant: negative imaginary part with positive real.

Common Pitfalls:

• Reversing axes (treating imaginary as horizontal) or using non-standard sign conventions.

Final Answer:
first quadrant