%* -------------------------------------------
%* mathsPIC 2.1
%* Copyright (c) RWD Nickalls 1999-2000
%* Email: dicknickalls@compuserve.com
%* Date (m/d/y) : 01-17-2001  15:28:44
%* Command Line: /s basipic1.m basipic1.tex
%* Input Filename:  basipic1.m
%* Output Filename: basipic1.tex
%* -------------------------------------------
%%%%
\input pictex
$$\beginpicture
%% paper{units(2cm,2cm),xrange(-2,2),yrange(0,2)}
\setcoordinatesystem units < 2cm, 2cm>
\setplotarea x from -2 to  2, y from  0 to  2
\axis left shiftedto y=0 ticks numbered
 from 1 to 2 by 1 /
\axis bottom  shiftedto x=0 ticks numbered from -2 to 0 by 1
 from 1 to 2 by 1 /
%% point(A){0,0}  ( 0 , 0 )
%% point(B){A,polar(1,0deg)}  ( 1 , 0 )
%% point(C){A,polar(1,0deg)}  ( 1 , 0 )
%% ... points C & B are the same
%point(z2){A,polar (1,45 deg)}
%point(z1){A,polar (1,30 deg)}
%point(z3){A,polar (1,75 deg) }
%% point(z4){A,polar(1.7,135deg)}  (-1.202082 , 1.202082 )
%% drawPoints(z4)
\put {$\bullet$} at -1.202082  1.202082  %% z4
%% drawLine(Az4)
\plot   0  0    -1.202082  1.202082 /  %% Az4
%% drawAngleArrow{angle(BAz4),radius(0.4),internal,anticlockwise}
\circulararc  135 degrees from  .4  0 center at  0  0
\arrow <1.5mm>  [0.5, 1] from  -.2038478   .34416 to -.2828427  .2828427
\setdashes
%% drawPerpendicular(z4,AB)
\plot  -1.202082  1.202082    -1.202082  0   /
\setsolid
%% text($\theta$){A,polar(0.5,70deg)}[bl]
\put {$\theta$} [bl]  at  .1710101  .4698463
%% text($z = x + i y = |z| (\cos \theta + i \sin \theta)$){z4,shift(0,.1)}[b]
\put {$z = x + i y = |z| (\cos \theta + i \sin \theta)$} [b]  at -1.202082  1.302082
%% text($y$){z4,shift(-.2,-.5)}[l]
\put {$y$} [l]  at -1.402082  .7020816
%% text($x$){A,shift(-.6,.1)}[b]
\put {$x$} [b]  at -.6  .1
 %text($z_1= \mathop{\rm cis}30^{\circ}$) {z1}[tl]
 %text($z_2= \mathop{\rm cis}45^{\circ}$) {z2}[bl]
 %text($z_3 = z_1 \cdot z_2 = = \mathop{\rm cis}75^{\circ}$) {z3, shift(.1,.1)}[bl]
 %drawLine(A z1)
 %drawLine(A z2)
 %drawLine(A z3)
 %DrawAngleArrow{angle(B A z1 ), radius(0.5), internal ,anticlockwise}
 %DrawAngleArrow{angle(B A z2 ), radius(0.65), internal ,anticlockwise}
\endpicture$$
 %%%tex{\bye}
%* ---------
%* PointNumber = 50
%* Number of points/variables used = 4
%* List of points/variables used:-
%* A,B,C,z4,
%* ---------