Complex Numbers

Complex Plane

Displaying complex numbers

  • High school
  • about 3 min
  • 1 of 18 in the family
Not started
-3-3i-2-2i-1-1i11i22i33iReIm2 + 2i

Real part a

a = 2

Imaginary part b

b = 2
z=2+2iz = 2 + 2i
∣z∣=22+22=2.828|z| = \sqrt{2^2 + 2^2} = 2.828

arg(z) = 45.0°

The complex plane extends the number line into 2D. The real axis (green) is horizontal, the imaginary (pink) is vertical. The purple vector IS the complex number – it has both direction and magnitude.