Instructions for use of complex calculator:

Return to the Math APIs page.

• After ...herokuapp.com above you should type /json/ followed by your complex expression using the syntax below. If you want the response to be html rather than json, simply omit /json from the address.
• SYNTAX:
  • spaces: These are legal - but discouraged - because %20 will replace each space after you hit return, thereby making the address uglier.
  • numbers:
    • real: This should be an integer or decimal but not a fraction, because "/" has special meaning in a URL. Do not include any commas in the number, even if it exceeds 1000. You may represent large or small numbers with E notation, using either E or e, but neither D not d, owing to the fact that the latter characters are used to represent division, as described below.
    • imaginary: This should be a real number (See above.) which multiplies (See below.) either i or j.
    • complex: This is a simple sum/difference (See below.) of a real number and an imaginary number. (See above.)
  • binary operations:
    • Parentheses: Their use is encouraged as with any calculation, especially if you are uncertain as to the order of operations (ie, "PEMDAS" or "BEDMAS"). Use () but neither [] nor {}.
    • Exponentiation: ** (recommended) or ^. The latter is discouraged because %5E will replace each instance of ^ after you hit return, thereby making the address uglier. This app evaluates serial exponentiation (for which there is no standard) from left-to-right, ie as is the standard for the other binary operations. For instance, this app evaluates 1 ** 2 ** 3 as 1, not 8. Use parentheses if you would like to evaluate serial exponentiation in a different manner.
    • Multiplication: Do this either by * or in an implied manner, ie with nothing separating the two numbers.
    • Division: Because "/" has special meaning in a URL, represent this operation either by div or DIV, or even d or D.
    • Addition: +
    • Subtraction: -
  • units:
    • You may use any of the following abbreviated forms of "base" metric units: kg (kilogram), m (meter), s (second), K (kelvin), and mol (mole). This list includes all SI base units except for ampere and candela, each of whose abbreviations (A or cd) would interfere with either the symbol for division ("d") or with the use of several unary functions listed below.
    • You may use any "derived" metric units, which are formed by multiplying or dividing the base metric units, but you may not use any of the special names that are usually used for the derived units (e.g., abbreviations for joule, newton, watt, or hertz).
    • Units are incorporated into your expression by multiplication, which you may indicate either explicitly (ie, with "*") or implicitly.
    • The standard rules apply to the use of units in mathematical expressions:
      • Only quantities with identical units may be added or subtracted.
      • When multiplying or dividing quantities with units, the unit of the result equals the corresponding operation of the units of the input quantities.
      • For non-"basic" unary functions (See below.), the argument should be dimensionless, as is the value. For all "basic" functions except for Phase and Sqrt, the unit of the value equals the unit of the argument. For Sqrt, the unit of the value equals the square root of the unit of the argument. For Phase, the value is dimensionless.
  • unary operations: Below are listed the available functions, most of which are explained here.
    • basic: Real, Imag, Abs, Phase, Conj, Sqrt
    • exponential and its inverses: Exp, Log, Log2, Log10
    • circular trigonometric : Cos, Sin, Tan, Sec, Csc, Cot
    • inverses of circular trig: Acos, Asin, Atan, Asec, Acsc, Acot
    • hyperbolic trigonometric: Cosh, Sinh, Tanh, Sech, Csch, Coth
    • inverses of hyperbolic trig: Acosh, Asinh, Atanh, Asech, Acsch, Acoth
• EXAMPLE without units:
  • expression: {cos^-1[1.2i(3 + i)] + 4/(5 - 6i)}^{7 + 8i}
  • how to type: (Acos(1.2i(3+i))+4d(5-6i))**(7+8i)
  • result: -179350.52181665212 - 95128.46772892449 i
• EXAMPLE with units:
  • expression: 3 m/s + 4 m/s² 5 s
  • how to type: 3mds+4mds**2*5s
  • result: 23 m/s

creator:  Peter Knipp
repo:  https://github.com/pknipp/complexCalculator