Operations with Complex Numbers. Aim: Add, subtract, multiply and/or divide complex numbers in order...
-
Upload
emilio-sturman -
Category
Documents
-
view
219 -
download
0
Transcript of Operations with Complex Numbers. Aim: Add, subtract, multiply and/or divide complex numbers in order...
![Page 1: Operations with Complex Numbers. Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify. Simplify: 1. 2x + 3y – x + y = x + 4y.](https://reader031.fdocuments.us/reader031/viewer/2022032104/56649c4e5503460f948f3f60/html5/thumbnails/1.jpg)
Operations with Complex Numbers
![Page 2: Operations with Complex Numbers. Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify. Simplify: 1. 2x + 3y – x + y = x + 4y.](https://reader031.fdocuments.us/reader031/viewer/2022032104/56649c4e5503460f948f3f60/html5/thumbnails/2.jpg)
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
Simplify:1. 2x + 3y – x + y
= x + 4y
2. (x + 3)(x – 3)
= x2 – 3x + 3x - 9
= x2 – 9
3.
( )
4. i2
![Page 3: Operations with Complex Numbers. Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify. Simplify: 1. 2x + 3y – x + y = x + 4y.](https://reader031.fdocuments.us/reader031/viewer/2022032104/56649c4e5503460f948f3f60/html5/thumbnails/3.jpg)
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
Adding complex numbers
Find the sum of 4 + 2i and 2 – 5i.
Keep the real numbers together,
keep the imaginary numbers together.
is similar toadding polynomials.
![Page 4: Operations with Complex Numbers. Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify. Simplify: 1. 2x + 3y – x + y = x + 4y.](https://reader031.fdocuments.us/reader031/viewer/2022032104/56649c4e5503460f948f3f60/html5/thumbnails/4.jpg)
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
4 + 2i + 2 - 5i 6 - 3i
![Page 5: Operations with Complex Numbers. Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify. Simplify: 1. 2x + 3y – x + y = x + 4y.](https://reader031.fdocuments.us/reader031/viewer/2022032104/56649c4e5503460f948f3f60/html5/thumbnails/5.jpg)
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
Subtracting complex numbers
+− −( )
subtracting polynomials.
is similar to
![Page 6: Operations with Complex Numbers. Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify. Simplify: 1. 2x + 3y – x + y = x + 4y.](https://reader031.fdocuments.us/reader031/viewer/2022032104/56649c4e5503460f948f3f60/html5/thumbnails/6.jpg)
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
Multiplying complex numbers is similar
to multiplying polynomials.
![Page 7: Operations with Complex Numbers. Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify. Simplify: 1. 2x + 3y – x + y = x + 4y.](https://reader031.fdocuments.us/reader031/viewer/2022032104/56649c4e5503460f948f3f60/html5/thumbnails/7.jpg)
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
The complex conjugate
is similar to
the radical conjugate.
( )
![Page 8: Operations with Complex Numbers. Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify. Simplify: 1. 2x + 3y – x + y = x + 4y.](https://reader031.fdocuments.us/reader031/viewer/2022032104/56649c4e5503460f948f3f60/html5/thumbnails/8.jpg)
Aim: Add, subtract, multiply and/or divide complex numbers in order to simplify.
Dividing complex numbers
is similar to
we just divided complex numbers.