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Transcript
```Warm up
Algebra II/Trig Honors
Unit 1 Day 7: Operations with Complex Numbers
Big Ideas: We use notation to be precise and use symbols to stand for numbers or expressions
that are difficult to represent.
Absolute value gives the magnitude of a number.
Topical Understanding: Imaginary numbers allow us to represent square roots of negative numbers.
When the imaginary unit i is raised to any power, it simplifies.
Objective: Use properties of imaginary numbers to simplify expressions and solve equations
Key Concept: Not all quadratic equations have real-number solutions. For example, x 2  1 .
An imaginary unit i was created to allow us to now take the square root of negative numbers.

i  1
Ex:

i 2  1
Ex: i 3
3
 
2
Example 1: Solve.
2 x 2  11  37
Definitions:
 Complex number - _____________________________________________________________

Imaginary number - ____________________________________________________________

Pure Imaginary number - ________________________________________________________
Sum and Difference of Complex Numbers

To add (or subtract) two complex numbers, _________________________________
____________________________________________________________________
Example 2: Write the expression as a complex number in standard form.
a. 8  i   5  4i 
b. 7  6i   3  6i 
c. 10  6  7i   4i
Example 3: Circuit components such as resistors, inductors, and capacitors all oppose the flow of
current. This opposition is called resistance for resistors and reactance for inductors and capacitors. A
circuit’s total opposition to current flow is impedance. All of these quantities are measured in ohms  .
The table shows the relationship between a component’s resistance or reactance and its contribution to
impedance. A seriescircuit is also shown with the resistance or reactance of each component labeled.
The impedance for a series circuit is the sum of the impedances for the individual components. Find
the impedance for the circuit shown above.
Multiplying Complex Numbers

To multiply two complex numbers, __________________________________________
Example 4: Write the expression as a complex number in standard form.
a. 4i 6  i 
b. 9  2i  4  7i 
Complex Conjugates

_____________________________________________________________________

_____________________________________________________________________
Example 5: Divide Complex Numbers
Write the quotient
7  5i
in standard form.
1  4i
Complex Plane

Horizontal Axis: ________________________

Vertical Axis: __________________________
Example 6: Plot the complex numbers in the same complex plane.
a. 3  2i
b.  2  4i
c. 3i
d.  4  3i
Absolute Value of a Complex Number

______________________________________
______________________________________
______________________________________
Example 7: Find the absolute value of the complex numbers.
a.  4  3i
HW: Page 45 #3-54 (M3), 60
b.
 3i
```
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