Complex Numbers (π)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 π
Imaginary Numbers
The imaginary number, denoted by π (not a βjββ¦) is the number whose square equals β1.
π2 = β1 or π = β1Complex numbers are the numbers in the form π + ππ where the real number is βπβ and the imaginary part is βππβ
Imaginary Numbers
Evaluate the radicals
1. β25 2. β2
Imaginary Numbers
Evaluate the radicals
3. β48
Complex Numbers
Write in standard form π + ππ
4. 3 β β16 5. 5 + β12
Complex Numbers
Write in standard form π + ππ
6. 15β β75
5
Add, Subtract Complex Numbers
1. Write in standard form π + ππ
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 + 3π + (β6 + 7π) 8. 5 + β36 β (2 β β49)
Multiply Complex Numbers
1. Write in standard form π + ππ
2. Multiply using standard distribution
3. Simplify if necessary
REMINDER: π2 = β1
Multiply Complex Numbers
Multiply
9. β49 β β4 10. 2π(5 β 3π)
Multiply Complex Numbers
Multiply
11. (5 β 2π)(β1 + 3π) 12. (3 + 2π)(3 β 2π)
Divide Complex Numbers
1. Write in standard form π + ππ
2. Multiply numerator and denominator by the
conjugate of the denominator (just like with
radicals)
3. Simplify if necessary
REMINDER: π2 = β1
Divide Complex Numbers
13. 6+5π
3π14.
2βπ
4+3π
Powers of π
π0 = π4 =
π1 = π5 =
π2 = π6 =
π3 = π7 =
Powers of π
Simplify
15. π27 16. π38
17. π401 18. π4003