Daily Check For each equation find the discriminant and the number of solutions.

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5.4 Complex Numbers (p. 272).

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Daily Check For each equation find the discriminant and the number of solutions.

Launched Object h(t) = -16t t + 80 a)How many seconds until the max height is reached? b)What will be the max height? c)How many seconds until the object hits the ground? 2 sec. 144 ft. 5 sec.

Math I Day 10 ( ) UNIT QUESTION: What is a quadratic function? Standard: MM2A3, MM2A4 Today’s Question: How do we take the square root of negative numbers? Standard: MM2N1.a, b, c, d

You can't take the square root of a negative number, right? When we were young and still in Math I, no numbers that, when multiplied by themselves, gave us a negative answer. Squaring a negative number always gives you a positive. (-1)² = 1. (-2)² = 4 (-3)² = 9

So here’s what the math people did: They used the letter “i” to represent the square root of (-1). “i” stands for “imaginary” So, does really exist?

Examples of how we use

Ex: Solve x 2 + 6x +10 = 0 a = b = c = 1 st 2 nd

Complex Numbers A complex number has a real part & an imaginary part. Standard form is: Real part Imaginary part Example: 5+4i

The Complex Plane Imaginary Axis Real Axis

Graphing in the complex plane

Adding and Subtracting (add or subtract the real parts, then add or subtract the imaginary parts) Ex:

Graphing in the complex plane

Absolute Value of a Complex Number The distance the complex number is from the origin on the complex plane. If you have a complex number the absolute value can be found using:

Graphing in the complex plane 2 5

Examples Which of these 2 complex numbers is closest to the origin? -2+5i

Try These!!! Which of these 2 complex numbers is closest to the origin? 3i3i

Practice Coach Workbook Page 21

Assignment Page 4 #16-21 Page 8 #6-10 Page 19 #1-10