Questions on Algebra: Complex Numbers answered by real tutors!

To draw the complex number , plot the point
(x,y) and connect it to the origin (,).

So to draw the complex number , we have 
and 

Now we plot the point (,) and connect it to
the origin (,).



now we draw a perpendicular down to the x-axis:



We label  and 



Now we calculate r by the Pythagorean equation:















So we label  as 



Next we indicate the angle @ by a curved line:



Now we determine the angle @ by any trig function

sin(@) = , cos(@) =  or tan(@) = 

If we use the last one we have

tan(@) = 

and since we know that 45° has tangent 1, we know
the reference angle is 45°, and since @ is in the
second quadrant, the actual angle is 180°-45°or 135°.



The trig form is 

r[cos(@) + i·sin(@)]

so we substitute and get:

[cos(135°) + i·sin(135°)]

and sometimes this is abbreviated as

cis(135°)

Edwin