# Difference between revisions of "TI-BASIC:Angle"

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angle(''z'') returns the [http://mathworld.wolfram.com/ComplexArgument.html complex argument] (also known as the polar angle) of the complex number ''z''. If ''z'' is represented as ''x''+i''y'' where ''x'' and ''y'' are both real, angle(''z'') returns R►Pθ(''x'',''y'') (which is equivalent to tanֿ¹(''y''/''x'') if x is nonzero). Also works on a list of complex numbers. | angle(''z'') returns the [http://mathworld.wolfram.com/ComplexArgument.html complex argument] (also known as the polar angle) of the complex number ''z''. If ''z'' is represented as ''x''+i''y'' where ''x'' and ''y'' are both real, angle(''z'') returns R►Pθ(''x'',''y'') (which is equivalent to tanֿ¹(''y''/''x'') if x is nonzero). Also works on a list of complex numbers. | ||

− | + | <div style="background: #FFF; border: 1px dashed #DDD; padding-left:1em; margin: 1em 0 1em 0; font-family:Arial Unicode MS; color: #000; letter-spacing:1.2pt;"> | |

angle(3+4i) | angle(3+4i) | ||

.927295218 | .927295218 | ||

R►Pθ(3,4) | R►Pθ(3,4) | ||

.927295218 | .927295218 | ||

− | + | </div> | |

When writing a complex number ''z'' in the form <math>re^{i\theta}</math> (or, equivalently, <math>r(\cos\theta+i\sin\theta)</math>), then <math>\theta</math> is equal to the value of angle(''z''), suitably reduced so that the result returned is in the interval <math>-\pi<\theta\leq\pi</math>. | When writing a complex number ''z'' in the form <math>re^{i\theta}</math> (or, equivalently, <math>r(\cos\theta+i\sin\theta)</math>), then <math>\theta</math> is equal to the value of angle(''z''), suitably reduced so that the result returned is in the interval <math>-\pi<\theta\leq\pi</math>. | ||

## Latest revision as of 22:33, 26 November 2017

**Command Summary**

Returns the complex argument of a complex number.

**Command Syntax**

angle(*z*)

**Menu Location**

Press:

- MATH to access the Math menu.
- RIGHT, RIGHT to access the CPX (complex) submenu
- 4 to select angle(, or use arrows.

TI-83/84/+/SE

2 bytes

angle(*z*) returns the complex argument (also known as the polar angle) of the complex number *z*. If *z* is represented as *x*+i*y* where *x* and *y* are both real, angle(*z*) returns R►Pθ(*x*,*y*) (which is equivalent to tanֿ¹(*y*/*x*) if x is nonzero). Also works on a list of complex numbers.

angle(3+4i) .927295218 R►Pθ(3,4) .927295218

When writing a complex number *z* in the form <math>re^{i\theta}</math> (or, equivalently, <math>r(\cos\theta+i\sin\theta)</math>), then <math>\theta</math> is equal to the value of angle(*z*), suitably reduced so that the result returned is in the interval <math>-\pi<\theta\leq\pi</math>.

The angle( command also works on Matrices, though not in any useful way: angle([A] will return a matrix of the same size as [A], but with all elements 0. If you plan to use this, **don't**: 0[A] does the same thing, but is smaller and not as questionable (because this behavior is clearly unintentional on TI's part, and may be changed in an OS update).