will let Karen know you ate three quarters outof a four quarter pie. A real number is a number that will describe a measurement likeweight, length and fluid. However, in none of the four concept can you see the squareroot of -1 fall into place. There exist a fifth concept which is referred to as a complexnumber. As mentioned earlier a complex number equation = a+bi. It is a real number withan imaginary number. Quadratic Formula and Imaginary numbersThroughout our lifetime, teachers have informed students that negative numberscannot be squared. With imaginary numbers we are able to do so. With a very simpleexample it can be shown how this is true. With an equation like y = x^2+ 4x+29, we canget the x intercept by using the quadratic equation. By following all appropriate steps youwill find out where the x intercepts are at. Roots are all places that a graph will touch thex intercept. The quadratic equation = -b+- square root of b^2-4(a)(c)/ 2(a). Therefore,x^2=a , 4x= b and 29 = c. -4+- square root of 4^2 - 4(1)(29)2(1)-4+- square root of 16-116 2-4+- square root of -100 2-4 +-10i 2=-2+-5iThe answer -2 +-5i, lets you know that it is a complex root, meaning that it doesnot touch the x intercept. By graphing the equation y=x^2+4x+29, you will see theparabolas location. This parabola will not touch the x intercept. This table will show youhow: i^1=ii^4=1 i^2=-1i^5=i i^3=-ii^6=iComplex Root and Complex Conjugate RootThis is an ongoing cycle that will help you solve problems that deal with i^npower. Another amazing technique you can use is when you are given a complex root andthe complex conjugate root and you need to derive the equation by the root given andcomplex root. A complex conjugate root is that exact opposite of a complex root. Forexample if you are given one complex root of 2-5i, and you are asked to find the equationyou simply multiply 2-5i by the conjugate...
