Lecture_39 - MA 265 LECTURE NOTES FRIDAY APRIL 18 Review of Complex Numbers Definitions Consider the quadratic equation az 2 bz c = 0 where a b and

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MA 265 LECTURE NOTES: FRIDAY, APRIL 18 Review of Complex Numbers Definitions. Consider the quadratic equation az 2 + bz + c = 0 where a , b , and c are real numbers. Formally, we can write the two roots of this equation as z =- b 2 a ± √ b 2- 4 ca 2 a . Recall that we may classify these roots using the discriminant b 2- 4 ac : two real roots one real root two imaginary roots if b 2- 4 ac > 0; b 2- 4 ac = 0; b 2- 4 ac < 0. When the discriminant b 2- 4 ac ≤ 0, we can express these roots in the form z = x + iy in terms of real numbers x =- b 2 a and y = ± p | b 2- 4 ac | 2 a . Here i = √- 1 is that number such that i 2 =- 1, i 3 =- i , i 4 = 1, etc. We call z a complex number , where x is the real part and y is the imaginary part of z . Just as we denote the collection of all real numbers by R , we denote the collection of all complex numbers by C . Addition of Complex Numbers. We can add and subtract complex numbers by keeping track of the real and imaginary parts: z = x + iy w = u + iv = ⇒ ( z + w = ( x + u ) + i ( y + v ) z- w = ( x- u ) + i ( y- v ) We have the following properties: • Identity: The complex number 0 = 0 + i 0 satisfies z + 0 = 0 + z = z . • Inverses: The negative of z = x + iy is- z = (- x ) + i (- y ). This satisfies z + (- z ) = 0....
View Full Document

This note was uploaded on 03/11/2010 for the course MA 261A 0026100 taught by Professor ... during the Spring '10 term at Purdue University Calumet.

Page1 / 3

Lecture_39 - MA 265 LECTURE NOTES FRIDAY APRIL 18 Review of Complex Numbers Definitions Consider the quadratic equation az 2 bz c = 0 where a b and

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online