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<!DOCTYPE html>
<html data-require="math graphie graphie-helpers math-format">
<head>
<meta charset="UTF-8" />
<title>Complex number polar form intuition</title>
<script src="../khan-exercise.js"></script>
<style>
.info-box .mini-button {
padding: 0px 5px;
width: 20px;
}
</style>
</head>
<body>
<div class="exercise">
<div class="problems">
<div>
<div class="vars">
<var id="DENOMINATOR">12</var>
<var id="ANGLE">randRange( 0, DENOMINATOR - 1 )</var> <!-- the angle of the complex number is ANGLE * (2 * DENOMINATOR) pi -->
<var id="RADIUS">randRange( 1, 10 )</var>
<var id="REAL">cos( ANGLE * PI * 2 / DENOMINATOR ) * RADIUS</var>
<var id="IMAG">sin( ANGLE * PI * 2 / DENOMINATOR ) * RADIUS</var>
<var id="REP">complexNumber( roundTo( 2, REAL ), roundTo( 2, IMAG ) )</var>
</div>
<p class="question">
Adjust the angle and radius of the <span class="hint_orange">orange</span> plotted complex number
to match the <span class="hint_blue">blue</span> plotted complex number <code><var>REP</var></code>.
</p>
<p>
How do these numbers affect the complex number they represent?
</p>
<div class="graphie">
graphInit({
range: [[-10, 10], [-10, 10]],
scale: 20,
tickStep: 1,
axisArrows: "<->"
});
drawComplexChart( 10, DENOMINATOR );
circle( [REAL, IMAG], 1 / 4, {
fill: KhanUtil.BLUE,
stroke: "none"
});
graph.currComplexPolar = new ComplexPolarForm( DENOMINATOR, 10 );
</div>
<div class="solution" data-type="complexNumberPolarForm">
[ <var>ANGLE</var>, <var>RADIUS</var> ]
</div>
</div>
</div>
</div>
</body>
</html>
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