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<!DOCTYPE html>
<html data-require="math math-format">
<head>
    <meta charset="UTF-8" />
    <title>Adding and subtracting complex numbers</title>
    <script src="../khan-exercise.js"></script>
</head>
<body>
    <div class="exercise">
    <div class="vars">
        <var id="A_REAL">randRange( -5, 5 )</var>
        <var id="A_IMAG">randRange( -5, 5 )</var>
        <var id="B_REAL">randRange( -5, 5 )</var>
        <var id="B_IMAG">randRange( -5, 5 )</var>
        <var id="OPERATION">randFromArray( [ "add", "subtract" ] )</var>
        <var id="OPERATOR">( OPERATION === "add" ? "+" : "-" )</var>
        <var id="ANSWER_REAL">
            ( OPERATION === "add" ? ( A_REAL + B_REAL ) : ( A_REAL - B_REAL ) )
        </var>
        <var id="ANSWER_IMAG">
            ( OPERATION === "add" ? ( A_IMAG + B_IMAG ) : ( A_IMAG - B_IMAG ) )
        </var>
        <var id="A_REP">
            complexNumber(A_REAL, A_IMAG)
        </var>
        <var id="B_REP">
            complexNumber(B_REAL, B_IMAG)
        </var>
        <var id="A_REP_COLORED">
            "\\color{" + ORANGE + "}{" + A_REP + "}"
        </var>
        <var id="B_REP_COLORED">
            "\\color{" + BLUE + "}{" + B_REP + "}"
        </var>
        <var id="A_REAL_COLORED">
            "\\color{" + ORANGE + "}{" + A_REAL + "}"
        </var>
        <var id="A_IMAG_COLORED">
            "\\color{" + ORANGE + "}{" + A_IMAG + "}"
        </var>
        <var id="B_REAL_COLORED">
            "\\color{" + BLUE + "}{" + B_REAL + "}"
        </var>
        <var id="B_IMAG_COLORED">
            "\\color{" + BLUE + "}{" + B_IMAG + "}"
        </var>
    </div>

    <div class="problems">
        <div>
            <p class="question"><var>OPERATION == "add" ? "Add" : "Subtract"</var> the following complex numbers:</p>
            <p>
                <code>
                    (<var>A_REP_COLORED</var>) <var>OPERATOR</var> (<var>B_REP_COLORED</var>)
                </code>
            </p>
            <div class="solution" data-type="complexNumberSeparate">
                [ <var>ANSWER_REAL</var>, <var>ANSWER_IMAG</var> ]
            </div>
            <div class="hints">
                <p>
                    Complex numbers can be <var>OPERATION</var>ed by separately <var>OPERATION</var>ing their real and imaginary components.
                </p>
                <p>
                    The real components of the two complex numbers are <code class="hint_orange"><var>A_REAL</var></code> and <code class="hint_blue"><var>B_REAL</var></code>, respectively,
                    so the real component of the result will be
                    <code>
                        <var>A_REAL_COLORED</var> <var>OPERATOR</var> \color{<var>BLUE</var>}{<var>negParens(B_REAL)</var>}
                    </code>,
                    which equals <code><var>ANSWER_REAL</var></code>.
                </p>
                <p>
                    The imaginary components of the two complex numbers are <code class="hint_orange"><var>A_IMAG</var></code> and <code class="hint_blue"><var>B_IMAG</var></code>, respectively,
                    so the imaginary component of the result will be
                    <code>
                        <var>A_IMAG_COLORED</var> <var>OPERATOR</var> \color{<var>BLUE</var>}{<var>negParens(B_IMAG)</var>}
                    </code>,
                    which equals <code><var>ANSWER_IMAG</var></code>.
                </p>
                <p>
                    The result is <code><var>complexNumber(ANSWER_REAL, ANSWER_IMAG)</var></code>; its real component is <code><var>ANSWER_REAL</var></code>
                    and its complex component is <code><var>ANSWER_IMAG</var></code>.
                </p>
            </div>
        </div>
    </div>
    </div>
</body>
</html>
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