Complex solutions are a way to have an actual answer for a negative root. We used this in our class when we faced negative roots in the quadratic function. Basically, **−**1 = i so we take out the negative of a root by making it into **i**. Honestly speaking, the first time I saw the complex solutions, I felt that there was no point in it. Since the complex solution was just a imaginary, it would make much more sense to leave the answer as no solution. But after some research, I found out that complex solutions are related in many fields in science and mathematics that relate to our lives. These include engineering, electromagnetism, quantum physic and many other fields. Engineers use complex numbers to create two dimension vectors that does not exist, to program computers. These fields were very complex and hard for me to understand but one thing I learned was that complex numbers are used in computer programming. Also, another purpose of complex numbers was to solve equations that cannot be solved but needed to be solved. An example for this would be measuring population. Population cannot be measured using fractions like 1/2 of a person, so there comes the need of imaginary numbers to be able to express the population in whole numbers. The equations is provided here, which I do not fully understand. This means a lot to us because our lives revolve around technology and computers today, and without complex numbers, we will not have such high technology.

**Citation**

Complex Numbers. (2010). Retrieved from http://www.mathsisfun.com/numbers/

complex-numbers.html

Loy, J. (1999). Imaginary Numbers. Retrieved from http://www.jimloy.com/algebra/

imaginar.htm

Tatone, D. (1999, April 19). Complex Numbers in Real Life. Retrieved from

http://www.math.toronto.edu/mathnet/questionCorner/complexinlife.html

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