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jok3333 [9.3K]
3 years ago
8

Which of the following is a solution of z^5 = 1 + √3 i?

Mathematics
1 answer:
nordsb [41]3 years ago
8 0

Answer:

Option 2 is right

Step-by-step explanation:

Given that

z^5=1+\sqrt{3} i

We can write this in polar form with modulus and radius

|z^5|= \sqrt{1+3} =2\\tan of Angle t =\sqrt{3} \\

Hence angle = 60 degrees and

|z^5|= 2(cos60+isin60)

Since we have got 5 roots for z, we can write 60, 420, 780, etc. with periods of 360

Using Demoivre theorem we get 5th root would be

5th root of 2 multiplied by 1/5 th of 60, 420, 780,....

z= \sqrt[5]{2} (cos12+isin12)\\z=\sqrt[5]{2} (cos84+isin84)\\\\z=\sqrt[5]{2} (cos156+isin156)\\\\z=\sqrt[5]{2} (cos228+isin228)\\\\z=\sqrt[5]{2} (cos300+isin300)\\

Out of these only 2nd option suits our answer

Hence answer is Option 2.

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Bethany paid $408.75 for a pair of diamond stud earrings. The sale price was $375. What is the Percent of Sales Tax she paid for
9966 [12]

Answer:

She paid 9% of sales tax

Step-by-step explanation:

The sale price of diamond = $375

Let x be percent of sales tax

So, amount of tax = x\% \times 375 = \frac{x}{100} \times 375 =3.75x

So, Amount including tax = 375+3.75x

We are given that Bethany paid $408.75 for a pair of diamond stud earrings.

So, 375+3.75x=408.75

3.75x=408.75-375

x=\frac{408.75-375}{3.75}

x=9

Hence She paid 9% of sales tax

5 0
3 years ago
john wanted to run a 26k marathon. He only completed 0.75 of it before having to stop . How many kilometers did he run
kvasek [131]

Answer:

19.5 kilometers

Step-by-step explanation:

to find how much he ran we can multiply the two numbers

26 * 0.75 is 19.5

he only ran 19.5 kilometers

6 0
3 years ago
What's the answer to -6<21
Sphinxa [80]

Answer:

Step-by-step explanation:

There's no answer here. Because -6<21.

5 0
3 years ago
A 5000 seat theater has tickets for sale at 26 and 40. How many tickets should be sold at each price for a sellout performance t
slavikrds [6]

Answer:

The number of tickets for sale at $26 should be 3300

The number of tickets for sale at $40 should be 1700

Step-by-step explanation:

Use 2 equations to represent the modifiers within the problem:

5000 = a + b \\ 153800 = 26a + 40b

Now you want to find the point at which the variables are changed to make both equations correct, this can be done by graphing and finding the intersection of both lines.

5000 = 3300 + 1700 \\ 153800 = 26(3300) + 40(1700)

5 0
3 years ago
Review the diagram below.
morpeh [17]

Answer:

the asnwer is 35°

Step-by-step explanation:

you can said bca and its gonna give you that

7 0
3 years ago
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