**iCalcula: Complex Numbers**

*December 3, 2017*

Complex numbers are stored in the memory stack using both Part1 and Part2. In |SYS| menu you can activate either |Complex in Cartesian| or |Complex in Polar| flag. Complex input mode flag is displayed in yellow at the top of the display and indicates the default mode for complex input. If you enter an number and press |i| (if Complex in Cartesian activated) or |θ| (if Complex in Polar activated) instead of |ENTER| key, the number is stored in Part1 of x-register as real part or modulus (depending on Cartesian or Polar mode), display is cleared and you can continue with the input of the complex number. If system flag "Complex in Cartesian" is activated a blue "/Im" label is displayed at the left of x-display to indicate that the imaginary part is being input., which will be stored in Part2. If system flag "Complex in Polar" is activated a blue "/θ" label is displayed to indicate that the argument is being input. The underscore "_" indicates you are in input mode. If your press on the blue label, x-display changes to Part1 and blue label indicates "/Re" or "/R" depending on Cartesian or Polar mode. Successive touches exchange displayed part of the complex number and you can continue editing its value while in input mode. You get out of input mode in the usual way: |ENTER| key or a function key.

The default angular mode system flag specifies which unit of measure to assume for angles used in complex argument input. To set an angular mode enter |SYS| menu and press |Angles in Radians| or |Angles in Degrees|. Default angular mode system flag is displayed in yellow at the top of the display. Explicit angular mode through unit specification (adimensional subunit in |UNIT| menu) in a numeric input overrides default angular mode.

Following operators perform computations on complex numbers:

|+| : Computes (y + x)-registers and stores result in x-register

|-| : Computes (y - x)-registers and stores result in x-register

|×| : Computes (y * x)-registers and stores result in x-register

|÷| : Computes (y / x)-registers and stores result in x-register

|1/x| : Computes inverse of x-register and stores result in x-register

|x²| : Computes square of x-register and stores result in x-register

|√x| : Computes square root of x-register and stores result in x-register

|y ˣ| : Computes power x-register of y-register and stores result in x-register

|ˣ√y| : Computes x-register root of y-register and stores result in x-register

|±| : Changes sign to x-register

Following groups of functions perform computations on complex numbers:

• Exponential and logarithmic functions

• Parts functions

• Power functions

• Trigonometric functions

• Hyperbolic functions

• Conversion functions

EXPONENTIAL AND LOGARITHMIC FUNCTIONS

|Exp| key enters Exponential menu with functions:

|e^x| : Natural exponential (base e)

|10^x| : Common exponential (antilogarithm)

|Log| key enters Logarithm menu with functions:

|ln(x)| : Natural logarithm (base e)

|log(x)| : Common logarithm (base 10)

PARTS FUNCTIONS

|Parts| key enters Parts menu with functions:

|Real Part| : Gives real part of a complex number

|Imaginary Part| : Gives imaginary part of a complex number

|Absolute Value| : Calculates |x-register|

|Argument Value| : Calculates argument of x-register

POWER FUNCTIONS

|yˣ| : y-register raised to a power of x-register

|ˣ√y| : root x-register of y-register

TRIGONOMETRIC FUNCTIONS

|Trig| key enters Trigonometric Functions menu with functions:

|Sin| : Sin(x-register)

|Cos| : Cos(x-register)

|Tan| : Tan(x-register)

|ArcSin| : ArcSin(x-register)

|ArcCos| : ArcCos(x-register)

|ArcTan| : ArcTan(x-register)

The default angular mode specifies which unit of measure to assume for angles used in trigonometric functions.

HYPERBOLIC FUNCTIONS

|Hyp| key enters Hyperbolic Functions menu with functions:

|Hyp Sin| : Hyperbolic Sin(x-register)

|Hyp Cos| : Hyperbolic Cos(x-register)

|Hyp Tan| : Hyperbolic Tan(x-register)

|Hyp ArcSin| : Hyperbolic ArcSin(x-register)

|Hyp ArcCos| : Hyperbolic ArcCos(x-register)

|Hyp ArcTan| : Hyperbolic ArcTan(x-register)

CONVERSION FUNCTIONS

|Conv| key enters Conversion Functions menu with functions:

|Cartesian to Polar| : Converts a complex number in x-register from cartesian to polar notation

|Polar to Cartesian| : Converts a complex number in x-register from polar to cartesian notation

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