pre-calc 2.1-2.2

pre-calc 2.1-2.2 - Section 2.1 Complex Numbers The...

This preview shows pages 1–4. Sign up to view the full content.

Section 2.1 Complex Numbers The imaginary unit , , is defined as , where Ex . 7 7 1 7 i = - = - i 4 16 1 16 = - = - *Complex Numbers : can be written in the form , referred to as standard form a = “real part” b = “imaginary part” Ex . i + 3 i i 5 0 5 + = i 0 6 6 + = *Equality of Complex Numbers : di c bi a + = + if and only if c a = and d b = Ex . i i 3 5 2 3 7 + = - + *Operations with Complex Numbers 1.) Adding : -when adding two (or more) complex numbers, just add the real parts and add the imaginary parts EX 1 : EX 2 : ) 2 7 ( ) 4 ( ) 3 1 ( i i i - + + - + + 2.) Subtracting : i d b c a di c bi a ) ( ) ( ) ( ) ( - + - = + - + EX 3: ) 7 3 ( ) 4 ( i i + - +

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

View Full Document
EX 4: ) 4 12 ( ) 6 2 ( i i - - + 3.) Multiplication : ) )( ( di c bi a + + use FOIL or distributive property EX 5: ) 9 2 ( 7 i i - EX 6: ) 7 6 )( 4 5 ( i i - + **Special case of Multiplication—Complex Conjugates EX 7: Multiply ) 2 1 )( 2 1 ( i i - + The complex conjugate of the number bi a + is , bi a - and vice versa. 2 2 2 2 ) )( ( b a b abi abi a bi a bi a + = + + - = - + 4.) Dividing – multiply the numerator and denominator by the complex conjugate of the denominator EX 8: Divide i i 3 4 4 3 + -
* Roots of Negative Numbers For any positive real number b, the principal square root of the negative number –b is defined by EX 10 : Perform the indicated operation 48 27 - + - EX 11: Perform the indicated operation ) 3 2 ( 8 + - - Section 2.2 Quadratic Functions

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern