Argument of -i

[AlphaWZW]

What is the argument of -i?

On an Argand diagram, there is only 1 line...

How you find the argument of -i without a real number?

[studiot]

An Argand Diagram show two axes, x and y.

 

It shows all numbers of the form x+iy,

 

When y=0 all the numbers are of the form x+i0 = x.

That is they are real numbers without an imaginary part.

So this represents the x axis.

 

When x=0 all the numbers are of the form 0+iy = iy.

This is, of course the y axis.

The numbers long this axis are purely imaginary they have no real part.

 

All other numbers are complex numbers with both an imaginary and a real part and they cover the rest of the complex plane represented by the Argand Diagram.

For any value of x, y the argument = arctan(y/x).or inverse tan(y/x)

 

So you are looking for angles that have a tangent of -1.

 

What angles do you know that have this value?

 

This angle then defines a line through the origin, but not including it, on the Argand Diagram, every point of which has y/x=-1.

I say not including the origin since this has no argument since you x=y=o and you can't form the quotient y/x.

 

How many of these will be complex and how many real?

Edited October 1, 2013 by studiot

[Amaton]

What is the argument of -i?

On an Argand diagram, there is only 1 line...

 

How would you write this in the form [math]a+bi[/math]? From there, you will know the real and the imaginary parts needed to find its argument.