MathMath

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Complex numbers

Re Im arg angle

Re(z) As in Mathcad

The real part of z.

Element by element for a vector or matrix. Im gives the imaginary part.

Units

Units are kept.

Re(3+4i)=3
Re(5⋅V)=5 V

Im(z) As in Mathcad

The imaginary part of z, as a real number.

Element by element for a vector or matrix. Re gives the real part.

Units

Units are kept.

Im(3+4i)=4
Im(7)=0

arg(z) As in Mathcad

The angle of z in radians, from −π to π.

Element by element for a vector or matrix. Divide by deg to see degrees. For a pair of numbers x and y rather than a complex number, see atan2; angle gives angles from 0 to 2π.

Units

The answer is in radians, and z can have units.

arg(1+1i)=0.785
arg(−1)=3.142

angle(x, y) As in Mathcad

The angle of the point (x, y), in radians from 0 to 2π.

Note the order: x first, then y. It differs from atan2 only below the x axis, where it gives angles above π instead of negative ones: angle(−1, −1) is 5π/4.

Refused

  • Complex or vector arguments.
angle(0,1)=1.571
angle(1,−1)=5.498