This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Professor P. Bishop MAC1105 (MDN) 1.3 Complex Numbers; Quadratic Equations with a Negative Discriminant The complex number system enables us to take even roots of negative numbers by means of the imaginary unit i , which is equal to the square root of –1; that is i 2 = 1 and i = 1 . By factoring –1 out of a negative expression, it becomes positive and an even root can be taken: b = i b . Standard form for complex expression is a + bi , where a is the real part and bi is the imaginary part. All properties of exponents hold when the base is i , thus i 1 = i, i 2 = 1, i 3 = i 2 (i) = 1i = i, i 4 = i 2 (i 2 ) = 1(1) = 1. In general, for i n , divide n by 4: if the remainder is 0, i n = 1 ; if the remainder is 1, i n = i , if the remainder is 2, i n = 1 ; if the remainder is 3, i n = i. The product of a complex number (a + bi) and its conjugate (a – bi) is a nonnegative real number (a 2 + b 2 )....
View
Full Document
 Fall '08
 Staff
 Equations, Negative Numbers, Complex Numbers, Complex number, Professor P. Bishop

Click to edit the document details