1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Bad White [126]
3 years ago
7

Which of the following are square roots of —8 + 8i/3? Check all that apply.

Mathematics
1 answer:
8090 [49]3 years ago
6 0

Answer:

Options (2) and (3)

Step-by-step explanation:

Let, \sqrt{-8+8i\sqrt{3}}=(a+bi)

(\sqrt{-8+8i\sqrt{3}})^2=(a+bi)^2

-8 + 8i√3 = a² + b²i² + 2abi

-8 + 8i√3 = a² - b² + 2abi

By comparing both the sides of the equation,

a² - b² = -8 -------(1)

2ab = 8√3

ab = 4√3 ----------(2)

a = \frac{4\sqrt{3}}{b}

By substituting the value of a in equation (1),

(\frac{4\sqrt{3}}{b})^2-b^2=-8

\frac{48}{b^2}-b^2=-8

48 - b⁴ = -8b²

b⁴ - 8b² - 48 = 0

b⁴ - 12b² + 4b² - 48 = 0

b²(b² - 12) + 4(b² - 12) = 0

(b² + 4)(b² - 12) = 0

b² + 4 = 0 ⇒ b = ±√-4

                     b = ± 2i

b² - 12 = 0 ⇒ b = ±2√3

Since, a = \frac{4\sqrt{3}}{b}

For b = ±2i,

a = \frac{4\sqrt{3}}{\pm2i}

  = \pm\frac{2i\sqrt{3}}{(-1)}

  = \mp 2i\sqrt{3}

But a is real therefore, a ≠ ±2i√3.

For b = ±2√3

a = \frac{4\sqrt{3}}{\pm 2\sqrt{3}}

a = ±2

Therefore, (a + bi) = (2 + 2i√3) and (-2 - 2i√3)

Options (2) and (3) are the correct options.

You might be interested in
Troy is going to Spain and needs to convert his dollars to euros. He knows that when he goes, $5.00 is equivalent to about 3.45
Annette [7]
125/5=25
25*3.45=86.25

86.25 euros

4 0
3 years ago
Read 2 more answers
Can someone help me with this math homework please!
Grace [21]

Answer:

4

Step-by-step explanation:

7h-15h+40=-72

-8h=-32

h=4

7 0
3 years ago
Twice c is equal to 44
Juliette [100K]

Answer:

C=44/2

c=22

Two time c is equal to 44

one time c is equal to 22

5 0
2 years ago
Solve each Multi-Step equation.<br> -6(-6n + 2)=-228
attashe74 [19]

Answer:gnhbk j bmnj

Step-by-step explanation:

5 0
3 years ago
Read 2 more answers
How many times did Emmy get her<br> hair cut in the year?
Setler79 [48]

Answer:

5

Step-by-step explanation:

3 0
3 years ago
Read 2 more answers
Other questions:
  • Which of the following is an equivalent function to the function below?
    13·1 answer
  • There are 10 sport balls in the equipment closet. Three or kick balls. Write the portion of the balls ever kick balls as a fract
    12·1 answer
  • What numbers add to 33 and muliplies to 75
    5·1 answer
  • Simplify the exprssion -3/6 minus 5/7
    13·2 answers
  • A philosophy professor assigns letter grades on a test according to the following scheme. A: Top 14% of scores B: Scores below t
    15·1 answer
  • -4.4=3.1+w/3 Solve for "W"
    5·2 answers
  • Please helpppppppppp
    5·1 answer
  • 4/25^1/2nnnmmmmmmmmmmmmmmmmmmmmmmm
    10·1 answer
  • Manny baked 48 cookies for a bake sale. 75% of the cookies were chocolate chip. How many cookies were NOT chocolate chip
    12·1 answer
  • Hi guys can l ask...... A BABY IS 3WEEKS AND 4 DAYS OLD. WHAT IS THE AGE OF THE BABY IN DAYS​
    12·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!