Complex Number Functions

The following functions are available to manipulate complex numbers. There is an example of each complex number function in the PipeDream Examples.

PipeDream usually uses 1 × 2 arrays to represent complex numbers.

The formula C_ADD({1,2},{3,4}) would return the result {4,6}.

Because ranges can be used instead of arrays, you could enter 1 in cell A1 and 2 in cell B1 then use C_ADD(A1B1,{3,4}).

If you enter the formula {A1,B1} in cell A2, you could use C_ADD(A2,{3,4}).

Each of these would produce the same result.

Revisions:

Starting with 4.58, PipeDream also allows the use of OpenDocument / Microsoft Excel-style complex number strings, where lower-case suffixes i or j denote the imaginary part. C_ROUND() may be used to produce strings of manageable length from the output of complex number functions.

Example:
"2-3i"

C_ACOS

Syntax:

C_ACOS(complex_number)

Returns the complex arc cosine of complex_number as a complex number.

C_ACOSEC

Syntax:

C_ACOSEC(complex_number)

Returns the complex arc cosecant of complex_number as a complex number.

C_ACOSECH

Syntax:

C_ACOSECH(complex_number)

Returns the complex hyperbolic arc cosecant of complex_number as a complex number.

C_ACOSH

Syntax:

C_ACOSH(complex_number)

Returns the complex hyperbolic arc cosine of complex_number as a complex number

C_ACOT

Syntax:

C_ACOT(complex_number)

Returns the complex arc cotangent of complex_number as a complex number.

C_ACOTH

Syntax:

C_ACOTH(complex_number)

Returns the complex hyperbolic arc cotangent of complex_number as a complex number.

C_ADD

Syntax:

C_ADD(complex_addend_1, complex_addend_2)

Returns the sum of complex_addend_1 and complex_addend_2 as a complex number.

C_ASEC

Syntax:

C_ASEC(complex_number)

Returns the complex arc secant of complex_number as a complex number.

C_ASECH

Syntax:

C_ASECH(complex_number)

Returns the complex hyperbolic arc secant of complex_number as a complex number.

C_ASIN

Syntax:

C_ASIN(complex_number)

Returns the complex arc sine of complex_number as a complex number.

C_ASINH

Syntax:

C_ASINH(complex_number)

Returns the complex hyperbolic arc sine of complex_number as a complex number.

C_ATAN

Syntax:

C_ATAN(complex_number)

Returns the complex arc tangent of complex_number as a complex number.

C_ATANH

Syntax:

C_ATANH(complex_number)

Returns the complex hyperbolic arc tangent of complex_number as a complex number.

C_COS

Syntax:

C_COS(complex_number)

Returns the complex cosine of complex_number as a complex number.

C_COSEC

Syntax:

C_COSEC(complex_number)

Returns the complex cosecant of complex_number as a complex number.

C_COSECH

Syntax:

C_COSECH(complex_number)

Returns the complex hyperbolic cosecant of complex_number as a complex number.

C_COSH

Syntax:

C_COSH(complex_number)

Returns the complex hyperbolic cosine of complex_number as a complex number.

C_COT

Syntax:

C_COT(complex_number)

Returns the complex cotangent of complex_number as a complex number.

C_COTH

Syntax:

C_COTH(complex_number)

Returns the complex hyperbolic cotangent of complex_number as a complex number.

C_DIV

Syntax:

C_DIV(complex_dividend, complex_divisor)

Returns the result of dividing complex_dividend by complex_divisor as a complex number.

C_EXP

Syntax:

C_EXP(complex_number)

Returns e to the power of complex_number as a complex number.

C_LN

Syntax:

C_LN(complex_number)

Returns the natural logarithm of complex_number as a complex number.

C_MUL

Syntax:

C_MUL(complex_multiplicand_1, complex_multiplicand_2)

Returns the result of multiplying complex_multiplicand_1 by complex_multiplicand_2 as a complex number.

C_POWER

Syntax:

C_POWER(complex_number1, complex_number2)

Returns the result of raising complex_number1 to the power of complex_number2 as a complex number.

C_RADIUS

Syntax:

C_RADIUS(complex_number)

Returns the modulus of complex_number as a real number.

C_ROUND

Syntax:

C_ROUND(complex_number {, digits:Number})

Separately rounds the components of complex_number to digits decimal places.

digits must be an integer, either positive or negative (which rounds to the left of the decimal point).

Revisions:

This function was added in 4.58.

C_SEC

Syntax:

C_SEC(complex_number)

Returns the complex secant of complex_number as a complex number.

C_SECH

Syntax:

C_SECH(complex_number)

Returns the complex hyperbolic secant of complex_number as a complex number.

C_SIN

Syntax:

C_SIN(complex_number)

Returns the sine of complex_number as a complex number.

C_SINH

Syntax:

C_SINH(complex_number)

Returns the hyperbolic sine of complex_number as a complex number.

C_SUB

Syntax:

C_SUB(complex_minuend, complex_subtrahend)

Returns the result of subtracting complex_subtrahend from complex_minuend as a complex number

C_TAN

Syntax:

C_TAN(complex_number)

Returns the tangent of complex_number as a complex number.

C_TANH

Syntax:

C_TANH(complex_number)

Returns the hyperbolic tangent of complex_number as a complex number.

C_THETA

Syntax:

C_THETA(complex_number)

Returns the parameter in radians of complex_number.

This function is similar to ATAN_2.