Complex plane

The complex plane (Argand diagram) plots a + bi as the point (a, b): real part across, imaginary part up. The conjugate a − bi is its mirror image in the real axis.

Re + ImComplex plane

📐 Formula

z = a + bi ↔ (a, b); z̄ = a − bi

✏️ Worked example

z = −2 + 3i sits in quadrant II; its conjugate −2 − 3i is in quadrant III.

🌍 Where it is used

Electrical engineering (AC circuits), signal processing.

❓ Quick check

Where is 4i plotted?

🏋️ Practice

EasyConjugate of 5 − 2i?

Answer: 5 + 2i

MediumPlot of −3 − i?

Answer: (−3, −1)

Challengez + z̄ for z = a + bi?

Answer: 2a