AlphaWZW Posted October 1, 2013 Share Posted October 1, 2013 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? Link to comment Share on other sites More sharing options...
studiot Posted October 1, 2013 Share Posted October 1, 2013 (edited) 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 1 Link to comment Share on other sites More sharing options...
Amaton Posted October 1, 2013 Share Posted October 1, 2013 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. Link to comment Share on other sites More sharing options...
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