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N76 [4]
2 years ago
14

Write the square roots of 49 i in ascending order of the angle.

Mathematics
1 answer:
Troyanec [42]2 years ago
8 0

Answer:

The square roots of 49·i in ascending order are;

1) -7·(cos(45°) + i·sin(45°))

2) 7·(cos(45°) + i·sin(45°))

Step-by-step explanation:

The square root of complex numbers 49·i is found as follows;

x + y·i = r·(cosθ + i·sinθ)

Where;

r = √(x² + y²)

θ = arctan(y/x)

Therefore;

49·i = 0 + 49·i

Therefore, we have;

r = √(0² + 49²) = 49

θ = arctan(49/0) → 90°

Therefore, we have;

49·i = 49·(cos(90°) + i·sin(90°)

By De Moivre's formula, we have;

r \cdot (cos(\theta) + i \cdot sin(\theta) )^{\dfrac{1}{2}}  =  \pm \sqrt{r} \cdot \left (cos\left (\dfrac{\theta}{2} \right ) + i \cdot sin\left (\dfrac{\theta}{2} \right ) \right )

Therefore;

√(49·i) = √(49·(cos(90°) + i·sin(90°)) = ± √49·(cos(90°/2) + i·sin(90°/2))

∴ √(49·i) = ± √49·(cos(90°/2) + i·sin(90°/2)) = ± 7·(cos(45°) + i·sin(45°))

√(49·i) = ± 7·(cos(45°) + i·sin(45°))

The square roots of 49·i in ascending order are;

√(49·i) = - 7·(cos(45°) + i·sin(45°))  and  7·(cos(45°) + i·sin(45°))

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Answer:

Step-by-step explanation:

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4 0
3 years ago
The 5th of 9 consecutive whole numbers whose sum is 153 is?
sergejj [24]

We can start this problem by finding out what the lowest consecutive number's value is (x). Since consecutive numbers are numbers that are 1 apart from each other, the sum of 9 consecutive numbers would look like


x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8)


Since we know that they equal 153,


x + (x+1) + (x+2) + (x+3) + (x+4) + (x+5) + (x+6) + (x+7) + (x+8) = 153


Now we combine like terms


9x + 36 = 153


Simplify


9x = 117


x = 13


Now, we need to find what the 5th consecutive number is equal to. The fifth consecutive number is (x+4), so 13 + 4 is 17, meaning that the 5th of 9 consecutive numbers that add up to 153 is 17.

4 0
3 years ago
Read 2 more answers
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Step-by-step explanation:

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find the exponential regression equation for the data points (-4, 0.75), (-2, 6), (3, 28), and (5, 162)
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8 0
3 years ago
Can anyone help me with dis
dolphi86 [110]

Answer:

Slope is 2.

Step-by-step explanation:

So to find slope, we need to take the change in the y value, and the change in the x value, and then divide them. This may be confusing, so here is just 3 formulas in 3 seperate steps that we use to find it:

Step 1 - x_2-x_1=change_.in_.x

Step 2 - y_2-y_1=Change_.in_.y

Step 3 - \frac{Change_. in_. y}{Change_.in_.x}=slope

So lets start by doing step one.

All we need is to look for two x values. Lets use 5 and 6:

6-5=1

So 1 is our change of x. This is our 1st step.

Next we can use 2 y values, note that these should be the 2 y values that go wiht the x values above. So this means we have to use -3 and -1:

-1-(-3) = 2

So 2 is our change in y. This is our 2nd step.

Now lets plug this into:

\frac{Change_. in_. y}{Change_.in_.x}=slope:

\frac{2}{1}  = 2

So our slope is 2. Completing our 3rd and final step.

Hope this helps!

7 0
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