24
randFromArray( [ true, false ] )
randRange(1, 10)
randRange(1, 10)
ANSWER_RADIUS * B_RADIUS
"\\blue{" + ANSWER_RADIUS + "}"
randRange( 0, DENOMINATOR - 1 )
ANSWER_ANGLE_NUMERATOR * PI * 2 / DENOMINATOR
"\\blue{" + piFraction(ANSWER_ANGLE, true) + "}"
"\\red{" + B_RADIUS + "}"
randRange(1, DENOMINATOR - 1)
B_ANGLE_NUMERATOR * PI * 2 / DENOMINATOR
"\\red{" + piFraction(B_ANGLE) + "}"
"\\red{" + polarForm(B_RADIUS, B_ANGLE, USE_EULER_FORM) + "}"
cos( B_ANGLE ) * B_RADIUS
sin( B_ANGLE ) * B_RADIUS
"{" + A_RADIUS + "}"
(ANSWER_ANGLE_NUMERATOR + B_ANGLE_NUMERATOR) % DENOMINATOR
A_ANGLE_NUMERATOR * PI * 2 / DENOMINATOR
"{" + piFraction(A_ANGLE, true) + "}"
"{" + polarForm(A_RADIUS, A_ANGLE, USE_EULER_FORM) + "}"
cos( A_ANGLE ) * A_RADIUS
sin( A_ANGLE ) * A_RADIUS
"{" + piFraction((A_ANGLE_NUMERATOR - B_ANGLE_NUMERATOR ) * PI * 2 / DENOMINATOR, true) + "}"
Divide the following complex numbers:
{\color{blue}z} = \dfrac{v}{\color{red}w} = \dfrac{A_REP}{B_REP}
{\color{blue}z} = \dfrac{v}{\color{red}w} = \dfrac{A_REP}{B_REP}
graphInit({
range: [ [ -10, 10 ], [ -10 ,10 ] ],
scale: 20,
tickStep: 1,
axisArrows: "->"
});
drawComplexChart( 10, DENOMINATOR );
label( [A_REAL, A_IMAG], "\\color{black} v", "left" );
circle( [A_REAL, A_IMAG], 1 / 4, {
fill: KhanUtil.BLACK,
stroke: "none"
});
label( [B_REAL, B_IMAG], "\\color{red} w", "right" );
circle( [B_REAL, B_IMAG], 1 / 4, {
fill: KhanUtil.RED,
stroke: "none"
});
graph.currComplexPolar = new ComplexPolarForm( DENOMINATOR, 10, USE_EULER_FORM );
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 === ANSWER_ANGLE_NUMERATOR &&
radius === ANSWER_RADIUS;
redrawComplexPolarForm(guess[0], guess[1]);
redrawComplexPolarForm(guess[0], guess[1]);
For the division of to polar forms we divide the absolute values and subtract the angle.
The 1st number, v = A_REP,
has angle A_ANGLE_REP
and absolute value A_RADIUS_REP.
The 2nd, {\red w} = B_REP,
the angle B_ANGLE_REP
and absolute value B_RADIUS_REP.
Thus of the result are
\dfrac{A_RADIUS_REP}{B_RADIUS_REP} = ANSWER_RADIUS_REP.
The difference of the angles is A_ANGLE_REP - B_ANGLE_REP = INTERMEDIATE_ANGLE_REP.
The angle INTERMEDIATE_ANGLE_REP is negative.
Thus, the angle here is INTERMEDIATE_ANGLE_REP + 2 \pi = ANSWER_ANGLE_REP
as we want it be positive.
The difference of the angles is A_ANGLE_REP - B_ANGLE_REP = ANSWER_ANGLE_REP.