Solution of 3x2 = 7x − 3?<br><br>

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

17/6 + 4/3 fractions

polet [3.4K]

Answer:

25/6

Step-by-step explanation:

I multiplied 4/3 by 2, so the new fraction is 8/6. You add 17/6 with 8/6, and you get 25/6. I hope you understand.

8 0

3 years ago

At the museum, the O'Rourke family bought 3 adult tickets and 2 children tickets for $23.50. The Patel family bought 2 adult tic

Tresset [83]

6.25 for each kids ticket and 11.75 for each adult ticket

4 0

3 years ago

Please help and look at pic

Sati [7]

Answer:

-49

Step-by-step explanation:

First you convert them in improper fraction then it comes

35/3 × -21/5

With the help of cross multiplication we get

7×-7

And then 7×-7 = -49

3 0

3 years ago

2/3 of the people in the group came in blue cars and 1/8 of them came in red cars they were 48 people in the group so how many p

vodka [1.7K]

Answer:

32 people came in blue cars and 6 people came in red cars

Step-by-step explanation:

Technically, all 48 people came in red or blue cars, but I'm assuming that's not what the question is asking.

To find how many people came in blue cars, we do 2/3*48 which is equal to 32 people.

To find how many people came in red cars, we do 1/8*48 which is equal to 6 people.

7 0

4 years ago

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