Presentation on theme: "COMPLEX ZEROS OF A QUADRATIC FUNCTION"— Presentation transcript:
1 COMPLEX ZEROS OF A QUADRATIC FUNCTION SECTION 2.7COMPLEX ZEROS OF A QUADRATIC FUNCTION
2 SQUARE ROOTS OF NEGATIVE NUMBERS Is a value we have dealt with up to now by simply saying that it is not a real number.And, up to now, we have dealt with the following equation by simply saying it has no solution:x2 + 4 = 0
3 DEFINITION OF ii 2 = - 1The number i is called an imaginary number. Imaginary numbers, along with the real numbers, make up a set of numbers known as the complex numbers.
4 COMPLEX NUMBERS Imaginary Real i 2i 5 -1 - 3i 2/3i 1/2 .7 5 -11/2 .7
5 COMPLEX NUMBERSAll numbers are complex and should be thought of in the form:a + biImaginary PartReal Part
6 COMPLEX NUMBERS a + bi Real Part Imaginary Part When b = 0, the number is a real number. Otherwise, the number is imaginary.
11 Writing the reciprocal of a complex number in standard form. Example:
12 Writing the quotient of complex numbers in standard form. Example:
13 Writing the quotient of complex numbers in standard form. Example:
14 POWERS OF ii1 = ii2 = - 1i3 = - ii4 = 1i5 = iand so on
15 QUADRATIC EQUATIONS WITH A NEGATIVE DISCRIMINANT Quadratic equations with a negative discriminant have no real solution. But, if we extend our number system to the complex numbers, quadratic equations will always have solutions because we will then be including imaginary numbers.