Download 3.17 Complex Numbers - Reduce Radicals and Square Root

3.17 Complex Numbers - Reduce Radicals and Square Root Method
Simplify the following radicals.
1.
56 =
3.
98 =
2.
4. 5
324 =
300 =
3.17 Complex Numbers – Reduce Radicals and Square Root Method
Simplify the following radicals.
1.
56 =
3.
98 =
2.
4. 5
324 =
300 =
Solve using the square root method.
5. x² – 49 = 0
6. 3x² – 27 = 0
7. x² – 48 = 0
8. 10x² – 60 = 20
Solve using the square root method.
5. x² – 49 = 0
6. 3x² – 27 = 0
7. x² – 48 = 0
8. 10x² – 60 = 20
imaginary unit - the square root of a negative
𝒊 = −𝟏
𝒊𝟐 = −𝟏
If 𝑟 is a positive real number, then
−𝑟 = 𝑖 𝑟
𝑖 𝑟
!
If r=2, then
and
−2 = 𝑖 2
= 𝑖 ! 𝑟 = −𝑟
𝑖 2
!
and
= 𝑖 ! 2 = −2
9. Simplify the radicals:
−49
−4
−25
−100
−50
−18
imaginary unit - the square root of a negative
𝒊 = −𝟏
𝒊𝟐 = −𝟏
If 𝑟 is a positive real number, then
−𝑟 = 𝑖 𝑟
𝑖 𝑟
!
If r=2, then
and
−2 = 𝑖 2
= 𝑖 ! 𝑟 = −𝑟
𝑖 2
9. Simplify the radicals:
−49
−4
−25
−100
−50
−18
!
and
= 𝑖 ! 2 = −2
10. Solve the quadratic equations:
2𝑥 ! + 11 = −37
2𝑥 ! + 32 = 0
𝑥 ! + 25 = 0
3𝑥 ! + 30 = 0
10. Solve the quadratic equations:
2𝑥 ! + 11 = −37
2𝑥 ! + 32 = 0
𝑥 ! + 25 = 0
3𝑥 ! + 30 = 0