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Complex numbers

Formula calculator can perform many calculations using complex numbers. These are numbers z=x + i y that have a real part x and an imaginary part y, where i is the square root of minus 1. Formula calculator defines the constant i to make it easy to create complex numbers. If a complex number is used in an expression then the result is also a complex number.

Creating complex numbers: There are two ways of creating a complex number. One is to use the function cmplx(x,y) which creates a complex number with real part x and imaginary part y. For example myNum=cmplx(3,-2) creates a complex number with real part equal to 3 and imaginary part -2.

The second method is to use the constant i in an expression. So we could also have written myNum=3-i*2 to create the same complex number. Formula calculator also shows complex results in this format.

Complex functions: Many of formula calculator 's functions operate on complex numbers. These are:

  • + - * / ! ^%
  • sin() asin() cos() acos() tan() cot() atan() atan2() acot()
  • radians() degrees()
  • sinh() asinh() cosh() acosh() tanh() atanh()
  • exp() log() ln() log10() pow() sqrt()
  • gamma() abs() int() frac() sign() mod()
  • cmplx() real() imag() conj()
  • range() plot() FourierTransform()
  • solve()
  • matrix() element() transpose() adjoint() det()

Note that min() and max() are only defined for real numbers. However, for complex numbers min() and max() operate on the number magnitudes.