How to graph on Argand Diagram?

θ is a variable.

When you graph stuff like 2 or 3i you just just one real and 1 imaginary axis but when you plot something like 2cosθ you need two real axes and when you plot 2isinθ you need 2 imaginary axes.

The plot for 2isinθ will look just just like the plot for 2sinθ except that it the axes will the imaginary instead of real.

2 or 3i are just points on the Argand plane and can be represented in 1-D, 2 + 3i is requires 2 dimensions, 1 real and 1 imaginary. On the other hand 2isinθ is an purely imaginary curve and needs 2 imaginary dimensions to be represented.

If you want to plot 2cosθ + 2isinθ it will be 4-D and look like

http://www.wolframalpha.com/input/?i=+2%28e^i%CE%B...

(I have used Euler's relation in the input)

On the other hand if θ is constant you will get a point as sinθ and cosθ are constant and the graph will be the same as that for constants.

PS I edited the answer a number of times to make it more understandable so there may be some grammatical errors.

Argand Diagram Plotter Online

z1 is a vector z1 = 5 + 6i Plot ingredient (5,6) Draw a line from beginning to point P(5,6) place an arrow head at P Now have vector OP in 1st quadrant. comparable technique for :- z2 = 3 - 2i in 4th quadrant z3 = - 7 + 4i in 2nd quadrant z4 = - 5 - 6i in third quadrant