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Numbers
Numbers are our way to quantify, label, and organize the world around us in a logical manner. However, the systems used to obtain this goal differ geographically, historically, and by relative utility. All questions pertaining to numbers, including historic labeling systems, bases of numerical systems, constants, and the various ways they're grouped together, should be placed into this category.
46,867 Questions
How would you solve an imaginary number with -31 as its exponent?
The following discussion is for complex numbers; this includes (pure) imaginary numbers as a special case. This type of powers (a complex number to the power of a real number) are very simple if you write the complex number in polar coordinates, specifying an absolute value and an angle. Raise the absolute value to the specified power, and multiply the angle by the power.
Example (writing on a piece of paper is clearer; it is difficult to represent some of the symbols here):
(1 + i)6 = [(square root of 2) angle (45 degrees)]
Square root of 2 to the power 6 is 8.
45 degrees x 6 = 270 degrees, which is the same as minus 90 degrees.
The result is, then, 8 at an angle of -90 degrees. Converting this back to rectangular coordinates, this is equal to -8i.
How do you read in words 2280336.31?
Two million, two hundred eighty thousand, three hundred thirty-six and thirty-one hundredths.
What are the prime numbers 100 through 200?
101 103 107 109 113 127 131 137 139 149 151 157 163 167 173 179 181 191 193 197 199.
Are there even numbers other than 2 that are composites?
Actually all the even numbers except 2 are composite. This is so because every even number except 2 is divisible by 2 and this means the number is composite.
What are the importance of number pi?
Your pie wouldn't be a circle, it'd be some random shape. god bless the greeks.
What are those number belong to the prime number?
All numbers that only have one and itself as factors are prime. So to tell if a number is prime simply find it's factors. If it has more than two factors than it is not a prime number.
What is 14.096 rounded to the nearest whole number?
14.096 rounded to the nearest whole number is 14. If the zero had been a 5 or more, the answer would be to round up to 15 as the nearest whole number. But it was less then 5, so remained at 14.
Is there still a point to rationalizing denominators?
Yes.
One area where it is particularly useful is integration (in calculus).
Let Anita's age now be x
If: (x-6)^2 = x+6 => x^2-12x+36 = x+6 => x^2-13x+30 = 0
Solving the above quadratic equation: x = 3 or x = 10
Therefore Anita's age now must be 10 years of age
What are two numbers that multiply to make 58?
There are infinitely many possible pairs. Two such are (1, 58) and (10, 5.8).
