5.4 – Complex Numbers. What is a Complex Number??? A complex number is made up of two parts – a real number and an imaginary number. Imaginary numbers.

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Presentation transcript:

5.4 – Complex Numbers

What is a Complex Number??? A complex number is made up of two parts – a real number and an imaginary number. Imaginary numbers are defined to be the square root of -1 a + bi Real PartImaginary Part

COMPLEX NUMBERS COMPLEX NUMBERS Main Rules Where i is imaginary

The Complex Number Plane 12-2 i 2i -i -2i Because a complex number is made up of a real and an imaginary value, the complex number plane is different than an xy coordinate plane. Say we want to know where 2 – 2i would be We would go left or right for the real part and up or down for the imaginary part.

You Try… Graph: 3 + 2i

Finding Absolute Value The Absolute Value of a complex number is the distance away from the origin on the complex number plane. Ex: |3 - 4i| |a + bi|= 5

Complex Number Operations Combining like terms (adding or subtracting) (5 + 7i) + (-2 + 6i) (Hint: treat the imaginary i like a variable) i Multiplying Complex Numbers (12i)(7i) 84 i 2 =84 (-1) = -84

You can FOIL Complex Numbers! (6 – 5i)(4 – 3i) = 24 – 20i -18i + 15i 2 24 – 38i + 15(-1) 24 – 15 – 38i 9 – 38i Now, try a couple on your own: A)(2 + 3i)(-3 + 5i)B)(4 – 9i)(4 + 3i) i43 – 24i

Write the quotient in standard form.

Finding Complex Solutions 4x +100=0