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3 years ago

Express the complex number in trigonometric form. 5 - 5i

Mathematics

2 answers:

bazaltina [42]3 years ago

6 0

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Hi my lil bunny!

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Lets do this step by step.

This is the trigonometric form of a complex number where $|z|$ is the modulus and $0$ is the angle created on the complex plane.

$z = a + bi = |z| (cos ( 0 ) + I sin (0))$

The modulus of a complex number is the distance from the origin on the complex plane.

$|z| = \sqrt{a^2 + b^2}$ where $z = a + bi$

Substitute the actual values of a = -5 and b = -5.

$|z| = \sqrt{(-5) ^2 + (-5) ^2}$

Now Find $|z|$ .

Raise - 5 to the power of 2.

$|z| = \sqrt{25 + (-5) ^2}$

Raise - 5 to the power of 2.

$|z| = \sqrt{25 + 25}$

Add 25 and 25.

$|z| = \sqrt{50}$

Rewrite 50 as 5^2 . 2 .

$|z| = 5\sqrt{2}$

Pull terms out from under the radical.

$|z| = 5\sqrt{2}$

The angle of the point on the complex plane is the inverse tangent of the complex portion over the real portion.

$0 = arctan (\frac{-5}{-5} )$

Since inverse tangent of $\frac{-5}{-5}$ produces an angle in the third quadrant, the value of the angle is $\frac{5\pi }{4}$ .

$0 = \frac{5\pi }{4}$

Substitute the values of $0 = \frac{5\pi }{4}$ and $|z| = 5\sqrt{2}$ .

$5\sqrt{2} ( cos( \frac{5\pi}{4}) + i sin (\frac{5\pi}{4}))$

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Hope this helped you.

Could you maybe give brainliest..?

❀*May*❀

kolbaska11 [484]3 years ago

6 0

Answer:

five square root two times the quantity cosine of five pi divided by four plus i times sine of five pi divided by four

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PLEASE HELP ASAP!!!!!!!!

Ne4ueva [31]

Answer:

The first 5 terms are;

-2, 2, 13,38 and 91

Step-by-step explanation:

Here, we want to write the first 5 terms of the sequence.

We already have the first term as 1

Now, we need the 2nd term

Putting two in place of n, we have ;

2f(1) + 3n

= 2(-2) + 3(2) = -4 + 6 = 2

For the 3rd term, put 3 in place of n

2f(2) + 3(3)

sine f(2) = 2, we have

2(2) + 9 = 4+ 9 = 13

For the fourth term, put 4 in place of n, we have

2f(3) + 3(4)

since f(3) = 13

we have; 2(13) + 12 = 26 + 12 = 38

For the 5th term, put 5 in place of n, we have

2f(4) + 3(5)

since f(4) = 38, we have

2(38) + 15 = 76 + 15 = 91

6 0

3 years ago

Let X be the number of accidents per week at the Hillsborough Street roundabout by the NCSU Bell Tower. Assume X varies with mea

Eduardwww [97]

Answer:

1) 0.1587 = 15.15% probability that x is less than 2

2) 7.64% probability that there are fewer than 100 accidents at the roundabout in a year

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the Central limit theorem.

Normal probability distribution

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .