Complex Numbers

Complex Argument

Angle of complex number in plane

  • High school
  • about 3 min
  • 4 of 18 in the family
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45.0°1.5+1.5i
a = 1.5
b = 1.5
arg⁡(z)=atan2(1.50, 1.50)=45.00°\arg(z) = \text{atan2}(1.50,\,1.50) = 45.00°
arg⁡(z)∈(−180°, 180°]\arg(z) \in (-180°,\, 180°]

The argument (phase) is the angle the vector z makes with the positive real axis. Change the sign of b – the argument becomes negative (clockwise rotation).