Complex Number Traps

Four errors that catch everyone once. Work through them before your lab.

Trap 1 of 4

Trap 1

Quadrant Error

A student needs to find the angle of z = −3 + 4j.

θ = tan⁻¹(b/a)

θ = tan⁻¹(4 / −3)

θ = −53.1° ✗

Re Im z = −3+4j −53.1° ✗

↑ What's wrong here?

Trap 2

Wrong Form for Addition

🔒 Complete Trap 1 to unlock.
Trap 3

Multiplication Cross-Terms Dropped

🔒 Complete Trap 2 to unlock.
Trap 4

Conjugate Misconception

🔒 Complete Trap 3 to unlock.

All four traps cleared.

Keep this reference handy during your lab.

Trap The mistake The fix
Quadrant error θ = tan⁻¹(b/a) for all quadrants Check the quadrant; add 180° if the real part is negative
Wrong form Adding directly in polar form Convert to rectangular before adding or subtracting
Dropped cross-terms Skipping FOIL in multiplication Expand all four terms; remember j² = −1
Conjugate Flipping both signs Only flip the imaginary sign