 # Section 5.4 Imaginary and Complex Numbers

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Section 5.4 Imaginary and Complex Numbers

Imaginary Numbers The result of a square root of a negative number.
To overcome this problem, the IMAGINARY UNIT “i” was created.

Complex Numbers Contains a real number and an imaginary number
Always written in the form a + bi  a is the real part, b is the imaginary part Examples: 7 + 2i 2.5 – 3i i ¼ + 2i 5 + 10i

Add the real parts, then add the imaginary parts Examples: (4+7i) + (-8 + 2i) (7-5i) + (12-4i) (12+6i) – (15-3i)

Practice Page 277, #18-28 even and #38-46 even

Multiplying Complex Numbers
Use the distributive property or FOIL, just as we did with real numbers (remember that i2 = -1) i(7+i) 2i(10-3i)

(4+i)(3+2i) (2+3i)(2-3i)

Practice with Multiplication
Page 278, #47-55 ALL

Division with Complex Numbers
Just like with square roots, we do not want to have a complex number in the denominator of a fraction, or division problem. Example: 5 3+4i To simplify this, we use the Complex Conjugate of the denominator.

The Complex Conjugate of any complex number (a+bi) is (a-bi). Examples: Complex Conjugate 7+4i 7-4i 12-3i 12+3i -9-2i -9+2i

5 3+4i Multiply by the complex conjugate of the denominator over itself

8 2+4i

5+3i 1-2i

-5-4i 6+7i

Practice Page 278, 56-63