Download Notes Over 5.4 Dividing Complex Numbers

Notes Over 5.4
Imaginary Numbers
i  1
 9  9   1  3i
121  11i
i 
2
  1
i  1
2
2
Notes Over 5.4
Solving a Quadratic Equation
Solve the equation.
1. x  16
2
x    16
x   4i
2. 5 y  40
2
5
5
y  8
y   8
y   4 2
y  2i 2
2
Notes Over 5.4
Solving a Quadratic Equation
Solve the equation.
3. r  4  8
2
4 4
r  4
r  4
r   2i
2
4.  2t  8  46
2
8 8
2
 2t  54
2 2
2
t  27
t    27
t   9  3
t  3i 3
Notes Over 5.4
Solving a Quadratic Equation
Solve the equation.
5. 3x  1  35
2
1 1
2
3x  36
3
3
2
x  12
x   12
x  4  3
t  2i 3
6. y  25  0
2
 25  25
y  25
y    25
y   5i
2
Notes Over 5.4
Adding and Subtracting Complex Numbers
Write the expression as a complex number in standard form.
7. 5  4i   7  2i 
12  6i
8.  6  3i   5  i 
 1  4i
9. i 
 5 
 6i 
 5  7i
Notes Over 5.4
Adding and Subtracting Complex Numbers
Write the expression as a complex number in standard form.
10. 12  8i  
 6i 
6 
6  2i
11. 6  7i    3  i 
3  8i
12. 12 
 8 
10i 
4  10i
Notes Over 5.4
Multiplying Complex Numbers
Write as a complex number in standard form.
13.  2i5  i 
 2i  2  10i
 10i 
2
14. 4i3  5i 
 20i  20  12i
12i
2
15. 2  3i 2  3i 
 9i  13
4  6i  6i 
2
Notes Over 5.4
Multiplying Complex Numbers
Write as a complex number in standard form.
16. 4  i  2  6i 
 8 24i  2i
 6i  2  26i
2
17. 5  3i   5  3i 5  3i 
2
2

25  15i 15i 9i  16  30i
18. 8  i 2  i 
1
16  8i  2i  i  15  10i
2
Notes Over 5.4
Dividing Complex Numbers
Write as a complex number in standard form.
6 1 i
19.
1 i 1 i
6  6i
2
i
1  i  i  1
36 36i

21
 3 3i
Notes Over 5.4
Dividing Complex Numbers
Write as a complex number in standard form.
5i
20.
2i
2  i 10i  5i
2
2  i 4  2i 2i 
 1i
2
15  10i

51
 1 2i
2
Notes Over 5.4
Dividing Complex Numbers
Write as a complex number in standard form.
2  3i
21.
5i
i
i
 3i
2i 
2
5i
3  2i

5
2
Notes Over 5.4
Dividing Complex Numbers
Write as a complex number in standard form.
1 i
22.
1 i
 1i
1  i 1 i  i 
1  i 1  i  i1i 2
 2i

2
2
 i
Notes Over 5.4