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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&equals;z&ExponentialE;It where π<tπ.

• 

From the previous definition, for an arbitrary complex number z&equals;x&plus;Iy, argument(z) >= 0 if 0y. Otherwise argument(z) < 0.

  

For the case where y&equals;0, argument(z) = 0 if 0x. Otherwise argument(z) = Pi.

Examples

argumentz&ExponentialE;I2&pi;3

23&pi;

(1)

argumentpolar2&comma;&pi;7

17&pi;

(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

&pi;

(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

 


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