1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = 1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> + <em>i </em>² + <em>i</em> ³)
… = 1 + <em>i </em>+ <em>i</em> ² (1 + <em>i</em> + <em>i</em> ² (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> + (-1) (1 + <em>i</em> ))
… = 1 + <em>i</em> + (-1) (1 + <em>i</em> - 1 - <em>i</em> )
… = 1 + <em>i</em>
<em />
Alternatively, notice that
1 - <em>i</em> ⁶ = (1 - <em>i</em> ) (1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵)
so that
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - <em>i</em> ⁶) / (1 - <em>i</em> )
Now, <em>i</em> ⁶ = (<em>i</em> ²)³ = (-1)³ = -1, so
1 + <em>i</em> + <em>i</em> ² + <em>i</em> ³ + <em>i</em> ⁴ + <em>i</em> ⁵ = (1 - (-1)) / (1 - <em>i</em> )
… = 2 / (1 - <em>i</em> )
Multiply the numerator and denominator by the conjugate of 1 - <em>i</em> :
… = 2 (1 + <em>i</em> ) / ((1 - <em>i</em> ) (1 + <em>i</em> ))
… = 2 (1 + <em>i</em> ) / (1² - <em>i</em> ²)
… = 2 (1 + <em>i</em> ) / (1 + 1)
… = 1 + <em>i</em>
Answer:
Explanation:
Both ranges <em>ABUT </em> at their <em>eastern </em>or E.N.E
I'd like to follow up with an <em>ANTECEDENT </em>question for the reporter
It is his sacred duty and his private interest to <em>BEGET</em> children and to train them to take his place
When you use a baseball bat to beat someone until he is unconscious, this is an example of when you <em>BLUDGEON</em> him.
Her thoughts were interrupted by a <em>CACOPHONY </em>of a sound, I heard a voice call out in agony.
The harbour is <em>CAPACIOUS</em> and secure, with a sufficient depth of water for the largest vessels.
Music is a means of <em>CATHARSIS</em> for her.
Her <em>COTERIE</em> of fellow musicians His films are admired by a small <em>COTERIE</em> of critics.
Only a <em>DEMAGOGUE </em>could persuade so many people to rebel against authority.
Even his misanthropy is only an inverted form of social solicitude. Her books are a sovereign remedy for depression and misanthropy.
-Pencils were first used in 1662.
-Graphite is a crystalline form of the element carbon with its atoms arranged in a hexagonal structure.
- HB is a graphite hardness/grading scale: the higher the number next to H, the harder and lighter/less dark the pencil lead is.
- The H stands for “hard.”
Answer:
4
Explanation:
Since it's a flippy number, we can set each digit into ababa
Since it can be divisible by 15, which means it can be divisible by both 5 and 3.
Since it is divisible by 5, the last digit will be either 0 and 5, but it cannot be 0 because 0 cannot be the first digit, so last digit must be 5.
So, ababa --> 5b5b5
It can also be divisible by 3. According to de divisibility rule of 3, if the sum of all digit is divisible by 3 then the number is divisible by 3.
Sum of all digits = 15 + 2b
it's divisible by 3 when b = 0,3,6,9
The answer is 4.
There are 4 such number.
Answer:
a. 99.30% of the woman meet the height requirement
b. If all women are eligible except the shortest 1% and the tallest 2%, then height should be between 58.32 and 68.83
Explanation:
<em>According to the survey</em>, women's heights are normally distributed with mean 63.9 and standard deviation 2.4
a)
A branch of the military requires women's heights to be between 58 in and 80 in. We need to find the probabilities that heights fall between 58 in and 80 in in this distribution. We need to find z-scores of the values 58 in and 80 in. Z-score shows how many standard deviations far are the values from the mean. Therefore they subtracted from the mean and divided by the standard deviation:
z-score of 58 in= = -2.458
z-score of 80 in= = 6.708
In normal distribution 99.3% of the values have higher z-score than -2.458
0% of the values have higher z-score than 6.708. Therefore 99.3% of the woman meet the height requirement.
b)
To find the height requirement so that all women are eligible except the shortest 1% and the tallest 2%, we need to find the boundary z-score of the
shortest 1% and the tallest 2%. Thus, upper bound for z-score has to be 2.054 and lower bound is -2.326
Corresponding heights (H) can be found using the formula
and
Thus lower bound for height is 58.32 and
Upper bound for height is 68.83