Rectangular form conversion: Express the polar-form complex number 40∠55° as its equivalent rectangular form (a + jb).

Introduction / Context:
Converting between polar (magnitude ∠ angle) and rectangular (a + jb) forms is essential for phasor arithmetic in AC circuits. Rectangular form is convenient for addition and subtraction; polar form is handy for multiplication and division.

Given Data / Assumptions:

• Magnitude M = 40.
• Angle θ = 55° (degrees).
• Use a = M * cosθ and b = M * sinθ for rectangular components.

Concept / Approach:

Apply trigonometric projections to map the polar vector onto the real and imaginary axes. Ensure the calculator is in degrees when using degree angles.

Step-by-Step Solution:

Verification / Alternative check:

Back-convert: magnitude √(22.94^2 + 32.76^2) ≈ 40; angle arctan(32.76/22.94) ≈ 55°, confirming correctness.

Why Other Options Are Wrong:

40 + j40 and 55 + j55 imply θ = 45° with different magnitudes. 45.88 + j65.52 corresponds to a magnitude much larger than 40.

Common Pitfalls:

Using radians inadvertently; swapping sin and cos; rounding too early leading to noticeable errors.

Final Answer:

22.94 + j32.76