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argument

complex argument function

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

argument(z)

Parameters

z

-

algebraic expression

Description

• 

The argument function returns the principal value of the argument of the complex-valued expression z.  This means that argument(z) = t specifies z = polarz&comma;t=z&ExponentialE;It where π<tπ.

• 

From the previous definition, for an arbitrary complex number z=x+Iy, argumentz&gt;0 if y&gt;0. If y<0, then argumentz<0.

  

For the case y=0, if y is the special floating-point value −0., argument returns a floating-point approximation to -Pi. For the case where y=0 but y is not equal to the special floating-point value −0., argumentz&equals;0 if x0 and otherwise argumentz&equals;π.

  

For more information about the special floating-point value −0., see Numeric Computation in Maple.

Examples

argumentz&ExponentialE;I2Pi3

2π3

(1)

argumentpolar2&comma;Pi7

π7

(2)

Consider the following examples.

For z<0, argument(z) is always negative.

argument12.1I3

−0.5880026035

(3)

argument12.1I3

−2.553590050

(4)

For 0<z, argument(z) is always positive.

argument12.&plus;1I3

0.5880026035

(5)

argument12.&plus;1I3

2.553590050

(6)

For z=0, argument(z) is zero or π.

argument12

0

(7)

argument12

π

(8)

For exact numbers and in other situations, argument returns an expression using arctan.

argument3&plus;4I

arctan43

(9)

See Also

arctan

evalc

initialfunctions

parameter

polar

Re

signum