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Finger [1]
3 years ago
5

PLEASE HELP!

Mathematics
1 answer:
hjlf3 years ago
4 0
Answer: I think I know it but I have no clue I'm just answering to earn points.
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Use​ DeMoivre's Theorem to find the indicated power of the complex number. Write the answer in rectangular form.
slava [35]

Answer:

After solving the power:

\bold{2(cos60^\circ+isin60^\circ)}

Rectangular form:

\bold{1+i\sqrt3}

Step-by-step explanation:

Given the complex number:

2(cos20^\circ+isin20^\circ)^3

To find:

The indicated power by using De Moivre's theorem.

The complex number in rectangular form.

Rectangular form of a complex number is given as a+ib where a and b are real numbers.

Solution:

First of all, let us have a look at the De Moivre's theorem:

(cos\theta+isin\theta )^n=cos(n\theta)+isin(n\theta )

First of all, let us solve:

(cos20^\circ+isin20^\circ)^3

Let us apply the De Moivre's Theorem:

Here, n = 3

(cos20^\circ+isin20^\circ)^3 = cos(3 \times 20)^\circ+isin(3 \times 20)^\circ\\\Rightarrow cos60^\circ+isin60^\circ

Now, the given complex number becomes:

2(cos60^\circ+isin60^\circ)

Let us put the values of cos60^\circ = \frac{1}{2} and sin60^\circ = \frac{\sqrt3}{2}

2(\dfrac{1}{2}+i\dfrac{\sqrt3}2)\\\Rightarrow (2 \times \dfrac{1}{2}+i\dfrac{\sqrt3}2\times 2)\\\Rightarrow \bold{1 +i\sqrt3 }

So, the rectangular form of the given complex number is:

\bold{1+i\sqrt3}

3 0
3 years ago
Pls help will give brainliest and 5star plss
BaLLatris [955]

Answer:

3. 8 and 9

4. root 50 and root 144 for they are able to be multiplied to get a whole number/integer

5. 36 feet for the area is calculated be side x side all sides are equal so a number that has a whole root is the number so 36

6. 6 as would be one of the sides of the square rug

Hope this helps. Pls give 5 star, thanks, and brainliest.


6 0
3 years ago
PLEASE HELP I GIVE THANKS
VashaNatasha [74]
It is an obtuse triangle because all of the sides are diffrent amount

5 0
3 years ago
Read 2 more answers
a family pass to the amusement park costs $54.using the distributive property , write an expression that can be used to find the
Mandarinka [93]
9 x 6 = 54 is this right I'll do distributive property next time
4 0
3 years ago
Read 2 more answers
Solve the system using elimination.
Molodets [167]

Answer:

(-1, 3)

Step-by-step explanation:

x - 5y = -16  [Equation 1]

-x + 3y = 10 [Equation 2]

<u>Adding both equations</u>

  • x - x - 5y + 3y = -16 + 10
  • -2y = -6
  • y = 3

  • x - 5(3) = -16
  • x - 15 = -16
  • x = -1

<u>Solution</u> : (-1, 3)

5 0
2 years ago
Read 2 more answers
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