complex
The complex number a + bi. Exact when a and b are.
a(number) -- real partb(number) -- imaginary part
Complex Numbers
polar
The complex number with modulus r and argument theta (radians).
r(number) --theta(number) -- radians
re
The real part of a complex number (also z.re).
z(complex) --
im
The imaginary part of a complex number (also z.im).
z(complex) --
conjugate
The complex conjugate a - bi. Also the conjugate of a quaternion.
z(complex) --
modulus
|z| = sqrt(a^2 + b^2), exact (a surd when irrational).
z(complex) --
modulusSq
|z|^2 = a^2 + b^2, exact.
z(complex) --
argument
The argument (angle) of z in radians, in (-pi, pi].
z(complex) --
toPolar
The modulus r and argument theta of z, as a record (z.r, z.theta).
z(complex) --
isReal
True if the imaginary part is zero.
z(complex) --
isImaginary
True if the real part is zero.
z(complex) --
mul
The product of two complex numbers (a plain number counts as complex). Also the product of two quaternions (not commutative: ij = k, ji = -k).
z(complex) --w(complex) --
div
The quotient z / w of two complex numbers.
z(complex) --w(complex) --
cexp
e^z for a complex z.
z(complex) --
clog
The principal natural logarithm of a complex z.
z(complex) --
csqrt
The principal square root of a complex z (also of a negative number).
z(complex) --
cpow
z^n for a whole-number n, exact when z is.
z(complex) --n(integer) --
croots
All n n-th roots of z, as a list.
z(complex) --n(integer) --