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3 years ago

Express each of the following in a+bi form. a)(2 +5i)+(4 +3i)b)(−1+2i) − (4 − 3i)c)(5+3i)(3 +5i)d)(1 +i)(2 − 3i) +3i(1− i) − i

Mathematics

1 answer:

juin [17]3 years ago

6 0

Answer:

a 6+ 8i

b -5 + 5i

c 34i

d 8 + i

Step-by-step explanation:

<em>Add them together </em>6 + 8i

<em>Add them together </em>-5 + 5i

<em>Multiply it out</em> 15 + 25i + 9i + 15 $i^{2}$

<em>Add them together ( $i^{2}$ = the number times -1) </em> 34i

<em>Multiply it out</em> (2 - 3i + 2i - 3 $i^{2}$ ) + (3i - 3 $i^{2}$ ) - i

<em>Add what is in the parenthesis together ( $i^{2}$ = the number times -1) </em>(5 - i) + (3 + 3i) - i

<em>Add them together </em>8 + i

You might be interested in

What is the greatest common factor of 343, 49, and 196? 49 14 7 343 3?

S_A_V [24]

From the prime factorization of 49, we get 7*7. From 196, we get <span>2*2*7*7. From 343, we get 7*7*7. The greatest "overlap" or common factors are 7*7, or 49.</span>

Thus, the greatest common factor is 49.

4 0

3 years ago

Which of the following choices is the standard deviation of the sample shown

lana66690 [7]

Answer: E. square root of 2

We can write that in shorthand as sqrt(2)

sqrt(2) = 1.41421 approximately

======================================================

Explanation:

Step 1)

Add up the values to get 18+19+20+21+22 = 100

Divide by n = 5, since there are 5 items in the list. So 100/n = 100/5 = 20

The sample mean is xbar = 20

--------------

Step 2)

Subtract the mean from each data value

18 - xbar = 18 - 20 = -2
19 - xbar = 19 - 20 = -1
20 - xbar = 20 - 20 = 0
21 - xbar = 21 - 20 = 1
22 - xbar = 22 - 20 = 2

The results we get are: -2, -1, 0, 1, 2

---------------

Step 3)

Square the results from the previous step

(-2)^2 = 4
(-1)^2 = 1
(0)^2 = 0
(1)^2 = 1
(2)^2 = 4

The results here are: 4, 1, 0, 1, 4

---------------

Step 4)

Add up those squares from the previous step: 4+1+0+1+4 = 10

Now divide by n = 5 to get 10/n = 10/5 = 2

The result 2 represents the population variance. Applying the square root to the population variance leads to the population standard deviation. So we end up with the final answer of sqrt(2). The answer is choice E.

sqrt(2) = 1.41421 approximately

---------------

Note: if you want the sample standard deviation, then you divide by n-1 = 5-1 = 4, but the other steps are the same as before.

7 0

3 years ago

y = 1/3 |x| -2 in words its y equals one third idk what |x| is called idk if its minus to or negitive 2... so any help will be g

soldi70 [24.7K]

Technically speaking, because the way you have the question written, in words the equation would be said as y equals one-thirds multiplied by the absolute value of x, then minus two. Properly saying as y equals two less that the product of one-third and the absolute value of x.
The absolute value is the distance away from 0 therefor the value would alway equal as a positive value. EX1: |21| = 21 EX2: |-21| = 21
even if you considered -2 within y=1/3|x|-2 as -2 being negative two instead of minus two, then it would be the same meaning in the case that you have written out in a mathematical equation format, but really because -2 comes after 1/3|x| and -2 is not in parenthesis then it would make more since to say minus two.

3 0

3 years ago

3.49 hectograms equals how many decigrams

klasskru [66]

Answer:

3490 decigram

Step-by-step explanation:

$1 \:hectogram = 1000 \:decigram\\\\3.49\: hectogram = x\: decigram\\\\Cross\:Muliply\\\\x = 3.49\times 1000\\\\x = 3490 \:decigram$

8 0

3 years ago

What pairs of angles in the figures below are verified angles

ankoles [38]

Answer: Option A and option B.

Step-by-step explanation:

By definition,t wo angles are vertical when they share the same vertex, this happen when two lines intersect each other. Therefore, they are opposite and equal.

The angles given in the options of the problem, whicht share the same vertex , are the following angles:

∠ATN and ∠RTD

∠BTD and ∠ATP

Then the answer is: Option A and option B.

6 0

3 years ago