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Complex Numbers (๐)LESSON 7.8
Objective
Evaluate the square root of a negative real
number
Add or Subtract complex numbers
Multiply or divide complex numbers
Evaluate the powers of ๐
Imaginary Numbers
The imaginary number, denoted by ๐ (not a โjโโฆ) is the number whose square equals โ1.
๐2 = โ1 or ๐ = โ1Complex numbers are the numbers in the form ๐ + ๐๐ where the real number is โ๐โ and the imaginary part is โ๐๐โ
Imaginary Numbers
Evaluate the radicals
1. โ25 2. โ2
Imaginary Numbers
Evaluate the radicals
3. โ48
Complex Numbers
Write in standard form ๐ + ๐๐
4. 3 โ โ16 5. 5 + โ12
Complex Numbers
Write in standard form ๐ + ๐๐
6. 15โ โ75
5
Add, Subtract Complex Numbers
1. Write in standard form ๐ + ๐๐
2. Combine like terms
real combines with real
Imaginary combines with imaginary
3. Simplify if needed
Add, Subtract Complex Numbers
Add or Subtract
7. 2 + 3๐ + (โ6 + 7๐) 8. 5 + โ36 โ (2 โ โ49)
Multiply Complex Numbers
1. Write in standard form ๐ + ๐๐
2. Multiply using standard distribution
3. Simplify if necessary
REMINDER: ๐2 = โ1
Multiply Complex Numbers
Multiply
9. โ49 โ โ4 10. 2๐(5 โ 3๐)
Multiply Complex Numbers
Multiply
11. (5 โ 2๐)(โ1 + 3๐) 12. (3 + 2๐)(3 โ 2๐)
Divide Complex Numbers
1. Write in standard form ๐ + ๐๐
2. Multiply numerator and denominator by the
conjugate of the denominator (just like with
radicals)
3. Simplify if necessary
REMINDER: ๐2 = โ1
Divide Complex Numbers
13. 6+5๐
3๐14.
2โ๐
4+3๐
Powers of ๐
๐0 = ๐4 =
๐1 = ๐5 =
๐2 = ๐6 =
๐3 = ๐7 =
Powers of ๐
Simplify
15. ๐27 16. ๐38
17. ๐401 18. ๐4003
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