Polar form conversion: Convert the rectangular complex number 6 + j6 into polar form (magnitude ∠ angle in degrees).

Introduction / Context:
Converting between rectangular and polar forms lets us pick the most convenient representation for circuit computations. Equal real and imaginary parts indicate a 45° angle in the first quadrant for positive values.

Given Data / Assumptions:

• Rectangular form: a = 6, b = 6 (first quadrant).
• Magnitude formula: M = √(a^2 + b^2).
• Angle formula: θ = arctan(b/a) in degrees for a > 0.

Concept / Approach:

Calculate magnitude and angle directly. Because a = b > 0, the angle should be 45°, serving as a quick sanity check.

Step-by-Step Solution:

Verification / Alternative check:

Back-conversion: a = M cosθ ≈ 8.48 * 0.707 ≈ 6; b = M sinθ ≈ 8.48 * 0.707 ≈ 6.

Why Other Options Are Wrong:

6∠45° has correct angle but wrong magnitude. 8.48∠90° has correct magnitude but wrong angle. 36∠45° has magnitude squared error (not how polar magnitude is defined).

Common Pitfalls:

Confusing RMS/peak ideas with complex magnitude; forgetting that equal components imply 45° in quadrant I.

Final Answer:

8.48∠45°