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;
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°))
The value of 9 is 9,000 (nine thousand)
The awnser is 20 quarters
Answer:
-163,840
Step-by-step explanation:
Because the pattern is -4 you just multiply it through until you get to the 8th term. ;)
There are a number of expressions that are equivalent to 10a+6.
To find them, you simply have to list the multiples of both 10 and 6.
10- 10 20 30 40 50 60 70 80 90 100
6- 6 12 18 24 30 36 42 48 54 60.
Then, when you multiply the fraction by anything, whether this is 2, 3 or 10, you just have to do this to both parts.
All of the following expressions are equivalent to 10a+6
20a+12, 30a+18, 40a+24, 50a+30, 60a+36, 70a+42, 80a+48, 90a+54, 100a+60
Or, if you're looking to simplfy, then you have to find a common multiple, which is 2. Therefore, 2 goes outside of the bracket, and you then have to divide 10 by 2 to find out what goes inside the brack. 10a/2= 5a. 6/2=3, therefore, in a bracket, it becomes 2(5a+3)
Hope this helps :)
