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astra-53 [7]
2 years ago
6

3+5i/-2+3i perform operation

Mathematics
1 answer:
melisa1 [442]2 years ago
4 0

Answer:

\dfrac{9}{13}-\dfrac{19}{13}i

Step-by-step explanation:

Remember i^2=-1

You are given the fraction \dfrac{3+5i}{-2+3i}

First, multiply the numerator and the denominator by -2-3i:

\dfrac{3+5i}{-2+3i}=\dfrac{(3+5i)(-2-3i)}{(-2+3i)(-2-3i)}=\dfrac{(3+5i)(-2-3i)}{(-2)^2-(3i)^2}=\dfrac{(3+5i)(-2-3i)}{4-9i^2}=\dfrac{(3+5i)(-2-3i)}{4+9}

This gives you 13 in denominator, now multiply two complex numbers in numerator:

(3+5i)(-2-3i)=-6-9i-10i-15i^2=-6-19i+15=9-19i

Thus, the initial fraction is

\dfrac{9-19i}{13}=\dfrac{9}{13}-\dfrac{19}{13}i

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I need to do this problem by completing the square . help please
sukhopar [10]

Answer:

the roots are n = 1 + √15 and n = 1 - √15

Step-by-step explanation:

In this case I would immediately rewrite n² - 2n - 5 = 10 as

n² - 2n                  = 10 + 5 = 15.

To complete the square:  Identify the coefficient of n (it is -2). Halve that, obtaining -1, square this result, and then add the outcome (1) to and subtract the outcome (1) to n² - 2n:

n² - 2n  <em>+ 1 - 1   </em>             = 15

Next, rewrite n² - 2n  + 1 as the square of a binomial:

(n - 1)² = 15

Finally, take the square root of both sides:

n - 1 = ±√15

so that the roots are n = 1 + √15 and n = 1 - √15

8 0
2 years ago
A team spent 20 mins on passing drills and 40 minuets ona shooting drill, what is the ratio of time spent on shooting drills to
aliya0001 [1]
20 minutes on passing .....40 minutes on shooting

ratio of time spent on shooting to passing....
these are not hard, u just have to pay attention to the wording...

the ratio of shooting to passing is 40/20 which reduces to 2/1 or 2:1 or
2 to 1 <===

but if it would have asked for passing to shooting, it would have been :
20/40 which reduces to 1/2 or 1:2 or 1 to 2

so ur answer is 2/1 or 2:1 or 2 to 1
6 0
3 years ago
Complete the square to re-write the quadratic function in vertex form:<br> y = x2+ 10x - 2
Blababa [14]

Answer:

<h3>             \bold{y=(x+5)^2-27}</h3>

Step-by-step explanation:

                                      y = x^2+ 10x - 2\\\\y = x^2+ 2\cdot x\cdot5+5^2-5^2 - 2\\\\y=(x+5)^2-25-2\\\\y=(x+5)^2-27

8 0
3 years ago
What is the slope of the line passing through the points (−3, 4) and (4, −1)?
Igoryamba
Note:
The slope of a straight line passing through the points (x₁, y₁) and (x₂, y₂) is 
m= \frac{y_{2}-y_{1}}{x_{2}-x_{1}}

The two given points are (-3,4) and (4,-1). Therefore the slope is
m= \frac{-1-4}{4-(-3)} = \frac{-5}{7}

Answer: - \frac{5}{7}

3 0
3 years ago
In an aquarium, there are 10 large fish and 5 small fish. Half of the large fish are red. One fish is selected at random. Find t
valkas [14]
Large fish:10
Small fish: 5
Total: 15
Large fish with red: 5
Probability: 5/15 or 1/3 or 33.333333%

Please mark brainliest if this helped
Thank you
6 0
2 years ago
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