What do imaginary solutions mean

What are imaginary solutions? Remember, imaginary solutions always come in pairs. To find the imaginary solutions to a function, use the Quadratic Formula.

Therefore, all the solutions are imaginary. To solve, this function can be factored like a quadratic equation. Accordingly, the question is what is an imaginary solution in math?

In Algebra 1, you found that certain quadratic equations had negative square roots in their solutions. When this occurs, the equation has no roots or zeros in the set of real numbers. The roots belong to the set of complex numbers, and will be called "complex roots" or "imaginary roots". Accordingly, we may wonder what is the difference between real and imaginary solutions?

Real numbers include all rational numbers numbers that can be written like fractions and all irrational numbers numbers that cannot be written like fractions. We won't go into all the details here, but imaginary numbers are all multiples of something called the imaginary unit, which we write with the letter i. In like manner what does 2 imaginary solutions mean? Because adding or subtracting zero yields the same response, having a discriminant value of zero would indicate only one real solution.

This is often called a "double solution" or "two equal solutions" The last scenario is when the discriminant is positive. Read full answer Thanks 6. Do you have your own answer or clarification? Email address. You answer. Your reply has been sent for moderation.

Are real solutions the same as zeros? Step-by-step explanation: They are all the same thing because they all occur when the quadratic equation is equal to zero. When real, the solutions occur as x-intercepts and when imaginary they occur as complex conjugates that are solutions of the quadratic equation when it is set equal to zero.

Is 0 0 infinite or no solution? Here is a problem that has an infinite number of solutions. Is the point a solution?

If the point lies on both lines, then it is a solution. Now, Luke Walsh, aka LukeSelfwalker added this to the mix. Click it for the live Desmos file. Wow, Awesome links Aaron. Thank you for the additional links and insight. This will help me complete the proof I am working on. And see the Axis of Symmetry that […]. I was driving home from Delaware yesterday and, for no discernible reason, started to think about representing the solutions to complex functions.

Inspired by this brilliance I was imagining functions from C to C as transformations of the plane. The reason to think of it this way, for me, was to be able to think of transformations of 2D numbers to 2D numbers. What are you leaving out? So I wanted to think about quadratic functions as mapping points to other points in some kind of predictable way, and to think about what maps to 0,0 — in other words, finding complex roots of parabolas.

The square centered at 0 with side length 8 got turned into this lovely, spirally swoosh. But most interestingly, I noticed that every point on the new swoosh was mapped there from 2 different input points — so when I tried to find what maps to 0,0 I would need to find two different points that got there.

I did happen to find the roots of that polynomial the points that got mapped to 0,0 but not in any systematic way. Next was the desire to get systematic about finding roots. If and only if a and k are both positive, then there are 2 complex roots. So a, h, and k are real numbers and a and k are positive. Here are the transformations, in the order they happen: First: -h shifts the whole plane to the left if h is positive and to the right if h is negative Second: squaring doubles the angle argument of each point and squares its distance from the center.

Third: multiplying by a dilates points away from the center by a factor of a. Fourth: adding k shifts everything to the right k units. Because k is a positive real number, and real numbers on the complex planes have no vertical component. To find what mapped to 0, 0 I had to undo the transformations in backwards order: First, shift everything to the left k units. When we combine two AC currents they may not match properly, and it can be very hard to figure out the new current.

The beautiful Mandelbrot Set part of it is pictured here is based on Complex Numbers. The Quadratic Equation , which has many uses, can give results that include imaginary numbers.

The Unit Imaginary Number, i , has an interesting property. It "cycles" through 4 different values each time we multiply:. And that leads us into another topic, the complex plane :.