Read the result
The horizontal coordinate is the real part; the vertical coordinate is the imaginary part. The vector from the origin gives modulus and argument.
Complex numbers
Argand Diagram Plotter
Place a complex number on the real-imaginary plane and read its modulus and angle from the picture.
Formula
z = a + bi, |z| = sqrt(a^2 + b^2), arg(z) = atan2(b, a)
Result
Worked substitution
The real part is the horizontal coordinate and the imaginary part is the vertical coordinate.
Where it helps
A quick visual check before multiplying, dividing, taking roots, or interpreting phasors.
Common slip
Arguments depend on the quadrant. Using atan(b/a) alone can put the angle in the wrong place; atan2 handles the quadrant.
Try it
Plot 3 + 4i, then -3 + 4i. The modulus stays the same, but the argument moves to a different quadrant.