MATM1544_lecture 11.pdf - The image part with relationship ID rId7 was not found in the file MATM1544 LECTURE 11 Simpifying expressions with complex

# MATM1544_lecture 11.pdf - The image part with relationship...

This preview shows page 1 - 5 out of 11 pages.

8/8/2015 1 The image part with relationship ID rId7 was not found in the file. T: +27(0)51 401 9111 | [email protected] | MATM1544 LECTURE 11 Simpifying expressions with complex numbers August 8, 2015 T: 051 401 9111 [email protected] CONTENT Simplifying expressions The real number line The complex plane Polar coordinates Writing a complex number in polar form Examples Exercises
8/8/2015 2 MORE COMPLICATED: Example 2: Simplify (1 − 2°)(2 + °) 1 + ° + (2 − °)(1 + °) To the standard form ± + °² . Solution: First the fraction: (1 − 2°)(2 + °) 1 + ° = (1 − 2°)(2 + °)(1 − °) (1 + °)(1 − °) = (2 − 4° + ° − 2° ³ )(1 − °) 1 − ° ³ = (2 − 3° − 2 −1 )(1 − °) 1 − (−1) = (4 − 3°)(1 − °) 2 . So now (1 − 2°)(2 + °) 1 + ° = (4 − 3°)(1 − °) 2 = 4 − 3° − 4° + 3° ³ 2 = 4 − 7° − 3 2 = 1 − 7° 2 .
8/8/2015 3 Next term: 2 − ° 1 + ° = 2 − ° + 2° − ° ³ = 2 + ° + 1 = 3 + °. And we have already (1 − 2°)(2 + °) 1 + ° = 1 − 2 , So that (1 − 2°)(2 + °) 1 + ° + (2 − °)(1 + °) = 1 2 7 2 ° + 3 + ° = 1 2 + 3 + 1 − 7 2 ° = 1 + 6 2 + 2 − 7 2 ° = 7 2 2 . NOW YOU DO ONE Simplify to the standard form: 2 − 3° 5 + ° 1 − ° 1 + ° .
8/8/2015 4 We can now add: 3 − ° + 1 + = 4 + ° subtract : 3 − °

#### You've reached the end of your free preview.

Want to read all 11 pages?

• Summer '20
• Complex number

### 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