randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 ) randRangeNonZero( -9, 9 )

What is a+b?

\begin{align*} a &= AX + AYi \\ b &= BX + BYi \end{align*}

graphInit({ range: 10, scale: 20, tickStep: 1, labelStep: 1, unityLabels: false, labelFormat: function( s ) { return "\\small{" + s + "}"; }, axisArrows: "<->" }); line( [0, 0], [AX, AY], { stroke: "#6495ed", arrows: "->" } ); line( [0, 0], [BX, BY], { stroke: "#28ae7b", arrows: "->" } ); var AF = 1 + 0.8 / sqrt( AX * AX + AY * AY ); label( [AF * AX, AF * AY], "\\vec a", { color: "#6495ed" } ); var BF = 1 + 0.8 / sqrt( BX * BX + BY * BY ); label( [BF * BX, BF * BY], "\\vec b", { color: "#28ae7b" } ); addMouseLayer(); graph.point = addMovablePoint({coord: [1,1], snapY: 1, snapX: 1 }); graph.line = addMovableLineSegment({ pointA: graph.point, coordZ: [0,0], fixed: true, extendedLine: true });
Drag the point to the sum of the wo given complex numbers
graph.point.coord
if (_.isEqual(guess, [[-5, 5], [5, 5]])) { return ""; } return abs( AX+BX - guess[0]) < 0.001 && abs( AY+BY - guess[1] ) < 0.001;

Sum the real and imaginary components separately.

a + b= (AX + BX) + (AY + BY)i

line( [BX, BY], [BX + AX, BY + AY], { stroke: "#6495ed", arrows: "->" } );

a + b = AX + BX + AY + BYi

line( [0, 0], [BX + AX, BY + AY], { stroke: "#ffa500", arrows: "->" } );