12
randRange( 1, DENOMINATOR - 1 )
randRange( 1, 9 )
cos( ANGLE * PI * 2 / DENOMINATOR ) * RADIUS
sin( ANGLE * PI * 2 / DENOMINATOR ) * RADIUS
complexNumber( roundTo( 2, REAL ), roundTo( 2, IMAG ) )
Adjust the absolute value and angle of the complex number \blue{z}
until it matches the number {\color{orange} w =REP}
.
graphInit({
range: [[-10, 10], [-10, 10]],
scale: 20,
tickStep: 1,
axisArrows: "<->"
});
drawComplexChart( 10, DENOMINATOR );
label( [REAL, IMAG], "\\color{orange} \\large w", "left" );
circle( [REAL, IMAG], 1 / 4, {
fill: ORANGE,
stroke: "none"
});
graph.currComplexPolar = new ComplexPolarForm( DENOMINATOR, 10 );
graph.currComplexPolar.color = BLUE;
redrawComplexPolarForm();
[
graph.currComplexPolar.getAngleNumerator(),
graph.currComplexPolar.getRadius()
]
var angle = guess[0];
var radius = guess[1];
if (angle === 0 && radius === 1) {
return "";
}
return angle === ANGLE && radius === RADIUS;
redrawComplexPolarForm(guess[0], guess[1]);
redrawComplexPolarForm(guess[0], guess[1]);
The given number {\color{orange} w =REP}
has absolute value
{\color{orange}RADIUS}
.
Move {\color{blue}z}
to the circle with radius {\color{orange}RADIUS}
.
By adjusting the angle, the point then reaches the correct position.