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You can't say that one point "comes after" another point in the same way that you can say that one number comes after another number you can't say that (4, 5) "comes after" (4, 3) in the way that you can say that 5 comes after 3. But x, y-points don't come in any particular order. When you learned about regular (that is, about "real") numbers, you also learned about their order on the number line. This graphability of complex numbers leads somewhere interesting. Plot the point just as you would a coordinate point on the coordinate planeįor instance, you would plot the complex number 3 − 2 i by converting the complex number into coordinate-point form (that is, into (3, −2) form), and then graphing in the usual way: starting at the origin, moving three units to the right along the x-axis, moving two units down parallel to the y-axis, and drawing a dot.Convert the complex number from " a + bi" summing (that is, additive) form to " ( a, b) coordinate form.
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using "Re" for the horizontal axis having real-number values, and using "Im" for the vertical axis having imaginary-number values.using the regular x for the horizontal axis, but use yi for the vertical axis.However, if we change what the axes stand for, we can plot complex numbers. In the discussion above, I repeatedly pointed out that complex solutions to a quadratic equation are not graphable in the x, y-plane, because all points on the x, y are pairs of real numbers.
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The connection between the Quadratic Formula, complex numbers, and graphing is illustrated in the table below: What is the connection between the Quadratic Formula, complex numbers, and graphing? (This is the definition of a "solution" it is a value that solves the equation, making it true.) However, this complex-valued answer will not be a graphable x-intercept of the graph. Your complex-valued answer is still a valid "zero" or "root" or "solution" for that quadratic equation, because, if you plug the answer value back into the quadratic equation, you'll get zero after you simplify. The values on the x, y-plane are real numbers, so the complex-valued solutions of the equation cannot be seen on the x-axis. "Solutions", "roots", and "zeroes" of a given quadratic equation are now no longer necessarily also " x-intercepts". The difference now is that you have solutions (from the Quadratic Formula) to the equation which are not graphable. Were you to graph the quadratic equation, your graph will still not cross the horizontal axis. Now, with complex numbers, when the Formula gives you a negative inside the root, you now can simplify that solution by using the imaginary and respond that the equation under question has no real-valued solution, but it does have a complex-valued solution.