A) You're wrong, Dunce.<quoted text>
rabbee: and don't forget to get, a sheet of graph paper. so you can draw, the vector for +1x ++1y.
I have worked out the details using the polar co-ordinate method and the law of parallelogram for vector addition and I didn't need graph paper.
I just did a simple mental analysis in minutes and caught you again.
When you plot the real and imaginary parts of z = x +jy, you don't plot the x and y parts. You have to plot x along the x-axis and jy along the y-axis.
Now, tan theta = y/x = jy/x
If x = y,
tan theta = j,
theta = tan^-1 j which is not 45.
B) Parallelogram method:
Draw the x-y axes.
Plot x on the axis and jy on the y-axis.
Drop a perpendicular to the base along the x-axis.
The angle made by the x-axis with the y-axis (perpendicular) is 90 degree.
Draw the resultant of the parallelogram in the x-y plane.
The angle made by the resultant with the x-axis is alpha.
The angle made by the base with the slant height is theta.
Since, the resultant of the 2 vector components is the angle bisector of the angle made by the base of the IIgm with its slant height, thus, alpha = theta/2
Now, the perpendicular = jy = y sin theta, extended base = b cos theta
Now, a right triangle is formed by the extended base of the parallelogram with the resultant (hypotenuse) and the perpendicular serving as altitude.
So, by Pythagorasí theorem, we get:
Resultant =(x^2 + y^2 + 2xy cos theta)^1/2
x + y =(2 x^2 + 2x^2 .1/1.412)= 2x^2(2 + 1/1.412)^1/2
If x = 1,
x + y = 2( 1 + 0.708)^1/2 = 2 x (1.708)^1/2 = 2 x 1.1 (approx)= 2.2