How do we determine absolute value of complex numbers? Do Now: Explain “absolute value.” What is...
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How do we determine absolute value of complex numbers? Do Now: Explain “absolute value.” What is the distance formula?
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Transcript of How do we determine absolute value of complex numbers? Do Now: Explain “absolute value.” What is...
How do we determine absolute value of complex
numbers?
How do we determine absolute value of complex
numbers?Do Now: Explain “absolute value.”
What is the distance formula?
Do Now: Explain “absolute value.”
What is the distance formula?
Absolute valueAbsolute value
The distance from the origin is absolute value.
Five is located 5 units from the origin, so the absolute value is 5.
Negative five is also located 5 units from the origin, so the absolute value is also 5.
Absolute value is always positive.
The distance from the origin is absolute value.
Five is located 5 units from the origin, so the absolute value is 5.
Negative five is also located 5 units from the origin, so the absolute value is also 5.
Absolute value is always positive.
How does this relate to complex numbers?
How does this relate to complex numbers?
Remember, we can plot complex numbers on a coordinate grid
We need to measure from zero to the point.
What is the magnitude of the vector?
Remember, we can plot complex numbers on a coordinate grid
We need to measure from zero to the point.
What is the magnitude of the vector?
MagnitudeMagnitude
What if we were to treat the vector as a hypotenuse?
Then we could use the Pythagorean Theorem
What if we were to treat the vector as a hypotenuse?
Then we could use the Pythagorean Theorem
The length of the blue line can be found by finding the sum of the squares of the vertical line and the horizontal line, and taking the square root.
h2 = leg2 + leg2
The length of the blue line can be found by finding the sum of the squares of the vertical line and the horizontal line, and taking the square root.
h2 = leg2 + leg2
Example:Example:
Ex. Ex.
€
= 9 + 25 = 34
€
3+ 5i = 32 + 52
3+4i3+4i
2–4i2–4i
ReviewReview
Absolute value is distance from the origin
The general formula to determine absolute value is:
There should NEVER be a minus between the two terms in this radical.
Absolute value is distance from the origin
The general formula to determine absolute value is:
There should NEVER be a minus between the two terms in this radical.€
a+ bi = a2 + b2
Summary/HWSummary/HW
How is this formula similar to the distance formula and the Pythagorean Theorem?
Pg 71, all
How is this formula similar to the distance formula and the Pythagorean Theorem?
Pg 71, all
