Positive/Negative and Odd/Even Functions

... Remarks: If any argument is nonnumeric, GCD returns the #VALUE! error value. If any argument is less than zero, GCD returns the #NUM! error value. One divides any value evenly. A prime number has only itself and one as even divisors. Examples: GCD(5, 2) equals 1 GCD(24, 36) equals 12 GCD(7, 1) equal ...

... Remarks: If any argument is nonnumeric, GCD returns the #VALUE! error value. If any argument is less than zero, GCD returns the #NUM! error value. One divides any value evenly. A prime number has only itself and one as even divisors. Examples: GCD(5, 2) equals 1 GCD(24, 36) equals 12 GCD(7, 1) equal ...

Complex numbers - The Open University

... and only if α = 0 or β = 0, which does apply to R, carries over to our new system. (Note the use of “or” in the “or both” sense.) It may disconcert you to see us play around with a symbol that behaves as though it were the square root of −1: it should because, as yet, we have given no formal definit ...

... and only if α = 0 or β = 0, which does apply to R, carries over to our new system. (Note the use of “or” in the “or both” sense.) It may disconcert you to see us play around with a symbol that behaves as though it were the square root of −1: it should because, as yet, we have given no formal definit ...

prime numbers, complex functions, energy levels and Riemann.

... puzzled people. To understand how the primes are distributed Gauss studied the number (x) of primes less than a given number x. Gauss fund empirically that (x) is approximately given by x/log(x). In 1859 Riemann published a short paper where he established an exact expression for (x). However, th ...

... puzzled people. To understand how the primes are distributed Gauss studied the number (x) of primes less than a given number x. Gauss fund empirically that (x) is approximately given by x/log(x). In 1859 Riemann published a short paper where he established an exact expression for (x). However, th ...

Self-study Textbook_Algebra_ch9

... Now we would like to generalise the concept of square root and cube root to higher order. If a number to the nth power (where n is an integer greater than 1) is equal to a, then this number is called the nth root of a. In other words, if x n = a , then x is called the nth root of a. The computation ...

... Now we would like to generalise the concept of square root and cube root to higher order. If a number to the nth power (where n is an integer greater than 1) is equal to a, then this number is called the nth root of a. In other words, if x n = a , then x is called the nth root of a. The computation ...

teaching complex numbers in high school

... Suppose that i ϵ R. Then we know that i is greater than zero, equal to zero, or less than zero. If we take i to be greater than zero, then i2 = i ∙ i > 0 since the product of two positive numbers is positive. That is, -1 > 0 which is false. Therefore, i cannot greater than 0. Similar contradictions ...

... Suppose that i ϵ R. Then we know that i is greater than zero, equal to zero, or less than zero. If we take i to be greater than zero, then i2 = i ∙ i > 0 since the product of two positive numbers is positive. That is, -1 > 0 which is false. Therefore, i cannot greater than 0. Similar contradictions ...

5 Complex Numbers and Functions

... Consider the polynomial equation x2 + 3x + 2 = 0. Since x2 + 3x + 2 = (x + 1)(x + 2), the two solutions are x = −1 and x = −2. Unfortunately not all such equations have (real number) solutions. For example, since x2 > 0 for all x ∈ R, x2 + 1 > 0 + 1 = 1 > 0 for all x ∈ R ⇒ x2 6= −1 for all x ∈ R. To ...

... Consider the polynomial equation x2 + 3x + 2 = 0. Since x2 + 3x + 2 = (x + 1)(x + 2), the two solutions are x = −1 and x = −2. Unfortunately not all such equations have (real number) solutions. For example, since x2 > 0 for all x ∈ R, x2 + 1 > 0 + 1 = 1 > 0 for all x ∈ R ⇒ x2 6= −1 for all x ∈ R. To ...

M19500 Precalculus Chapter 1.2: Exponents and Radicals

... To talk about other powers, we need to define the parts of a power expression. 106 is the 6th power of 2. In the symbol 106 , 10 is the base and 6 is the exponent. However, some people refer to 6 as the power. Power expressions don’t need to involve numbers. For example xm is the mth power of x. If ...

... To talk about other powers, we need to define the parts of a power expression. 106 is the 6th power of 2. In the symbol 106 , 10 is the base and 6 is the exponent. However, some people refer to 6 as the power. Power expressions don’t need to involve numbers. For example xm is the mth power of x. If ...