randRangeNonZero(-5, 5)
randRangeNonZero(-5, 5)
randRangeNonZero(-5, 5)
randRangeNonZero(-5, 5)
Let a and b be complex numbers:
\begin{align*}
a &= REAL1 + COMPLEX1i \\
b &= REAL2 + COMPLEX2i
\end{align*}
What is a+b?
graphInit({
range: 11,
scale: 20,
tickStep: 1,
labelStep: 1,
});
label([ 11, 1], "Re", "left");
label([ 0.5, 10], "Im", "right");
line([0, 0], [REAL1, COMPLEX1], { stroke: "#6495ed", arrows: "->" });
line([0, 0], [REAL2, COMPLEX2], { stroke: "#28ae7b", arrows: "->" });
var AF = 1 + 0.8 / sqrt(REAL1 * REAL1 + COMPLEX1 * COMPLEX1);
label([AF * REAL1, AF * COMPLEX1], "a", { color: "#6495ed" });
var BF = 1 + 0.8 / sqrt(REAL2 * REAL2 + COMPLEX2 * COMPLEX2);
label([BF * REAL2, BF * COMPLEX2], "b", { color: "#28ae7b" });
addMouseLayer();
graph.guessPoint = addMovablePoint({
constraints: {},
snapX: 0.5,
snapY: 0.5,
});
Drag the orange point to plot your answer.
graph.guessPoint.coord
if (guess[0] === ANSWER[0] && guess[1] === ANSWER[1]) {
return true;
} else {
return false;
}
graph.guessPoint.setCoord(guess);
[REAL1 + REAL2, COMPLEX1 + COMPLEX2]
Sum the real and imaginary components separately.
a + b = (REAL1 + REAL2) + (COMPLEX1 + COMPLEX2)i
line([REAL2, COMPLEX2], [REAL1 + REAL2, COMPLEX1 + COMPLEX2], { stroke: "#6495ed", arrows: "->" });
graph.guessPoint.toFront();
\hphantom{a + b} = REAL1 + REAL2 + COMPLEX1 + COMPLEX2i
line([0, 0], [REAL1 + REAL2, COMPLEX1 + COMPLEX2], { stroke: "#ffa500", arrows: "->" });
graph.guessPoint.toFront();
graph.guessPoint.moveTo(REAL1 + REAL2, COMPLEX1 + COMPLEX2);
[REAL1 - REAL2, COMPLEX1 - COMPLEX2]
What is a-b?
Subtract the real and imaginary components separately.
a + b = (REAL1 - REAL2) + (COMPLEX1 - COMPLEX2)i
line([REAL1, COMPLEX1], [REAL1 - REAL2, COMPLEX1 - COMPLEX2], { stroke: "#28ae7b", arrows: "->" });
graph.guessPoint.toFront();
\hphantom{a + b} = REAL1 - REAL2 + COMPLEX1 - COMPLEX2i
line([0, 0], [REAL1 - REAL2, COMPLEX1 - COMPLEX2], { stroke: "#ffa500", arrows: "->" });
graph.guessPoint.toFront();
graph.guessPoint.moveTo(REAL1 - REAL2, COMPLEX1 - COMPLEX2);