MATHEMATICS COLLEGE

Write the complex number in the form a + bi. 8(cos 30° + i sin 30°)

Answers

Answer 1
Answer:

Answer:

4√(3) +4i

Step-by-step explanation:

Use the Euler's Formula, which is given by:

r e^(i \theta) = r(cos(\theta)+i sin(\theta))

Where:

a=rcos(\theta)\nb=rsin(\theta)\n\ntan(\theta)=(b)/(a)

From the problem, you can see:

r=8\n\theta=30^(\circ)

So:

a=8*cos(30)=4 √(3) \approx6.928\nb=8*sin(30)=4

Therefore, the complex number in its rectangular form is:

4√(3) +4i
Answer 2
Answer:

Answer:

4√(3)+4i

Step-by-step explanation:

8(\cos 30^\circ + i \sin 30^\circ) = 8 (√(3))/(2)+i8(1)/(2)=4√(3)+4i

Related Questions

Right or leftMost people are right-handed, and even the right eye is dominant for most people. Molecular biologists have suggested that late-stage human embryos tend to turn their heads to the right. In a study reported in Nature (2003), German bio-psychologist OnurGüntürkün conjectured that this tendency to turn to the right manifests itself in other ways as well, so he studied kissing couples to see which side they tended to lean their heads while kissing. He and his researchers observed kissing couples in public places such as airports, train stations, beaches, and parks. They were careful not to include couples who were holding objects such as luggage that might have affected which direction they turned. For each kissing couple observed, the researchers noted whether the couple leaned their heads to the right or to the left. They observed 124 couples, ages 13–70 years. Suppose that we want to use the data from this study to investigate whether kissing couples tend to lean their heads right more often than would happen by random chance.​The symbol π represents the long-run proportion of all the couples that lean their headsleftrightwhile kissing.Which of the following best describes the null hypothesis and the alternative hypothesis using π?null: π ≠ 0.5, alternative: π > 0.5null: π = 0.5, alternative: π < 0.5null: π = 0.5, alternative: π > 0.5null: π ≠ 0.5, alternative: π < 0.5Of the 124 kissing couples, 80 were observed to lean their heads right. What is the observed proportion of kissing couples who leaned their heads to the right? What symbol should you use to represent this value? (Round answer to 3 decimal places, e.g. 5.275)p^=the absolute tolerance is +/-0.001Determine the standardized statistic from the data. ​(Hint: You will need to get the standard deviation of the simulated statistics from the null distribution.) (Round answer to 2 decimal places, e.g. 52.75)z = the absolute tolerance is +/-0.02Interpret the meaning of the standardized statistic.The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations above the null hypothesized value of 0.50.The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations away from the null hypothesized value of 0.50.The observed proportion of couples who leaned to the right when kissing is 3.22 standard deviations below the null hypothesized value of 0.50.Select the best conclusion that you would draw about the null and alternate hypotheses.We have strong evidence that the proportion of couples that lean their heads to the right while kissing is more than 50%.We have strong evidence that the proportion of couples that lean their heads to the right while kissing is less than 50%.We have strong evidence that the proportion of couples that lean their heads to the right while kissing is 50%.We have strong evidence that the proportion of couples that lean their heads to the right while kissing is near to 50%.
Evaluate k - m if k = 8, m = -7, and p = -10.
Help me with this question pleasereee
If 25% is 14, what is 100%?
Victor collects data on the price of a dozen eggs at 8 different stores.median: $ 1.55Find the lower quartile and upper quartile ofthe data set.lower quartile: $upper quartile: S?$1.39 $1.40 $1.44 $1.50 $1.60 $1.63 $1.65 $1.80

if you are just given the two points it is the same formula. Find the midpoint between the points (4,−5) and (−4,5).

Answers

Answer:

M = (0,0)

Step-by-step explanation:

Given

(4,-5) and (-4,5)

Required

The midpoint (M)

This is calculated as:

M = (1)/(2)(x_1 + x_2,y_1+y_2)

So, we have:

M = (1)/(2)(4-4,-5+5)

M = (1)/(2)(0,0)

M = (0,0)

Brian has $88 and he saves $3.50 a week how many more weeks will it take him to get to 200​

Answers

Answer:

32 weeks

Step-by-step explanation:

First you should write an equation for this word problem. Since you know Brian wants to save to $200, the equation will equal 200. Then you figure out how much he has already, which is 88. Right now, the equation we have is 88+(weekly savings)= 200. He saves 3.50 a week, so the equation will finally look like 88+3.50x=200. X is how many weeks it will take for him to reach 200. We then move everything so that it all equals X. You would move the 88 first which will then give 3.50x=112. Dividing by 3.50 on both sides would give X as 32. SO the number of weeks it will take for Brian to save to $200 is 32 weeks.

I NEED HELP PLEASE, THANKS! :)

Answers

Answer:

D. No solution

Step-by-step explanation:

Instead of solving everything I just plugged the numbers on equations and saw that for some of them the numbers satisfied one or two equation but not all.  Also for some I saw that a number set makes the equation have no solution. For eg, I plugged option B into equation 3 and got 1305=756 which is never true so it is no solution.

Hope you understand :)

C) Which of these numbers is a square number?
A B C D
4х 10 9x 10* 4x 10 9x 10​

Answers

Answer:

could you put the choices in order for me to help you out please

What is the product of the expressions? Assume y does not equal 0.

Answers

Answer:

The correct answer would be option 4

12x+20

 5y3

Hope that helps.Thank you!!!

The radius of the large sphere is double the radius of thesmall sphere.
How many times is the volume of the large sphere than the
small sphere?
2
VX
O 4
O 6
O 8

Answers

Answer:

4 times as great

Step-by-step explanation:

Compute the two different volumes and then compare them.

Smaller sphere:  V = (4/3) · π ·r²

Larger sphere:  V = (4/3) · π · (2r)²     = (4/3) · π · 4 · r²

Comparing these, one sees immediately that the volume of the larger sphere is 4 times as great as that of the smaller sphere.
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