<span><span>The answer to the question is:</span></span>
<span><span /></span><span><span>−<span>12</span><span>(x−12)</span></span>
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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 )](https://tex.z-dn.net/?f=r%20%5Ccdot%20%28cos%28%5Ctheta%29%20%2B%20i%20%5Ccdot%20sin%28%5Ctheta%29%20%29%5E%7B%5Cdfrac%7B1%7D%7B2%7D%7D%20%20%3D%20%20%5Cpm%20%5Csqrt%7Br%7D%20%5Ccdot%20%5Cleft%20%28cos%5Cleft%20%28%5Cdfrac%7B%5Ctheta%7D%7B2%7D%20%5Cright%20%29%20%2B%20i%20%5Ccdot%20sin%5Cleft%20%28%5Cdfrac%7B%5Ctheta%7D%7B2%7D%20%5Cright%20%29%20%5Cright%20%29)
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°))
Answer:
5%, 33%, 1/2, 75%
Step-by-step explanation:
5% , 33%, 75%, 1/2
Change 1/2 to a percent.
1/2 = 0.5 = 0.5 * 100% = 50%
We are comparing
5%, 33%, 75%, 50%
From least to greatest:
5%, 33%, 50%, 75%
Now we convert 50% back to a fraction.
5%, 33%, 1/2, 75%
Answer:
2597
Step-by-step explanation: