Four errors that catch everyone once. Work through them before your lab.
Trap 1 of 4
A student needs to find the angle of z = −3 + 4j.
θ = tan⁻¹(b/a)
θ = tan⁻¹(4 / −3)
θ = −53.1° ✗
↑ What's wrong here?
A student needs to add 5∠30° and 3∠60°.
5∠30° + 3∠60°
= (5 + 3)∠(30° + 60°)
= 8∠90° ✗
↑ What's wrong here?
A student multiplies (2 + 3j)(1 + 2j).
(2 + 3j)(1 + 2j)
= 2×1 + 3j×2j
= 2 + 6j²
= 2 + 6(−1)
= −4 ✗
↑ What's wrong here?
A student needs the complex conjugate of z = 3 + 4j.
z = 3 + 4j
z* = −3 − 4j ✗
↑ What's wrong here?
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 |