Help with a complex number question, please. (1 Viewer)

[The Savior]

Express in the mod-arg form where θ is in radians: -3i
I get that the argument is equal to 3pi/2 (sorry I cant do the symbol for pi), but the answer says that the argument is -pi/2.
Could someone please explain why it is negative. Much thanks.

 

[Queenroot]

graph it

 

[rumbleroar]

because the negative sign determines the direction of the complex number, e.g. rotating something by "-" would mean its rotated 180 degrees
e.g. if i = pi/2, -i = 3pi/2 or -pi/2 when we consider the args must exist between -pi and +pi

 

[Axio]

It's because principle arg is defined from -pi<=x<=pi. Moving from positive x-axis to the positive y-axis is a movement of pi/2. So to go the reverse, moving from positive x axis to the negative y axis must be a movement of -pi/2. 3i = 3cispi/2 and -3i =3cis-pi/2, you will get these results if you put them in the calculator.

 

[dan964]

Calculating Mod-Arg Form

here is my trick to calculate mod-arg form and vice versa using fx82AU+ or fx100AU+

Use the Pol() function to find polar coordinate of a point (x,y) where z=x+iy
The modulus (r) is stored under the variable X, and the angle (theta) is stored under Y

Use Rec() for the reverse process. (r, theta) where z=r cis theta
gives (x,y) stored under X and Y respectively.


You can use a similar method for auxiliary angle method.

 

[HeroicPandas]

^delete your post before the police comes

 

[The Savior]

so the argument can be expressed as either 3pi/2 or -pi/2

 

[seventhroot]

so the argument can be expressed as either 3pi/2 or -pi/2

yes but -Pi/2 is more "right" because we take arguments to be between Pi

 

[Trebla]

so the argument can be expressed as either 3pi/2 or -pi/2

yes but -Pi/2 is more "right" because we take arguments to be between Pi

There are actually infinitely many arguments basically -pi/2 + 2kpi for some integer k. It's just that the principal arguments are just nicer to deal with. An answer of 3pi/2 is also correct as is 7pi/2 or 11pi/2.

 

[braintic]

Provided there is no follow-on question where principal arguments might be useful, 3pi/2 is perfectly fine and is no less 'right' than -pi/2.

 

[Joshmosh2]

Calculating Mod-Arg Form

here is my trick to calculate mod-arg form and vice versa using fx82AU+ or fx100AU+

Use the Pol() function to find polar coordinate of a point (x,y) where z=x+iy
The modulus (r) is stored under the variable X, and the angle (theta) is stored under Y

Use Rec() for the reverse process. (r, theta) where z=r cis theta
gives (x,y) stored under X and Y respectively.


You can use a similar method for auxiliary angle method.

woah, so OP. Thanks!