Introduction to Complex Numbers. Summary
... and it is given the name imaginary unit. It is standard to denote it by the single letter i (or j if i is being used for something else, such as for electric current in Electrical Engineering). Note that z = (x, y) = x(1, 0) + y(0, 1) = x1 + yi. We usually write z = x + iy. It is often significantly ...
... and it is given the name imaginary unit. It is standard to denote it by the single letter i (or j if i is being used for something else, such as for electric current in Electrical Engineering). Note that z = (x, y) = x(1, 0) + y(0, 1) = x1 + yi. We usually write z = x + iy. It is often significantly ...
Numbers & Operations
... hamburgers for $2.00, hotdogs for $1.50 and drinks for $1.00. Half of the money raised will go towards the purchase of team uniforms. If they sell 21 hamburgers, 34 hotdogs, and 65 drinks, how much money will they have to put towards the purchase of uniforms? A. $60 C. $120 ...
... hamburgers for $2.00, hotdogs for $1.50 and drinks for $1.00. Half of the money raised will go towards the purchase of team uniforms. If they sell 21 hamburgers, 34 hotdogs, and 65 drinks, how much money will they have to put towards the purchase of uniforms? A. $60 C. $120 ...
Problem Fields in Elementary Arithmetic
... Working with problems and making investigations is an activity one has to learn already very early or better said one has to preserve it from early childhood. Therefore in primary school children should not only learn concepts and solve given tasks for example with using algorithms for computing wit ...
... Working with problems and making investigations is an activity one has to learn already very early or better said one has to preserve it from early childhood. Therefore in primary school children should not only learn concepts and solve given tasks for example with using algorithms for computing wit ...
COMMON factors
... GREATEST COMMON the GREATEST (largest) number (factor) for both numbers FACTOR: (GCF) ...
... GREATEST COMMON the GREATEST (largest) number (factor) for both numbers FACTOR: (GCF) ...
orthogonal arrays application to pseudorandom numbers generation
... elements from {0,..,L-1} each combination of t columns contains without repetition all Lt combinations of numbers {0,..,L-1}. OA may be used for generation of pseudorandom sequences using enumeration of combinations of columns and writing their rows in line. This results in very long not repeated se ...
... elements from {0,..,L-1} each combination of t columns contains without repetition all Lt combinations of numbers {0,..,L-1}. OA may be used for generation of pseudorandom sequences using enumeration of combinations of columns and writing their rows in line. This results in very long not repeated se ...
pmwc-problems
... numbers 1 to 8. If A is the largest number amongst A, B, C and D, what is A? 12. A nine-digit number abcdefghi is such that its digits are all distinct and non-zero. The two-digit number ab is divisible by 2, the three-digit number abc is divisible by 3, the four-digit number abcd is divisible by 4, ...
... numbers 1 to 8. If A is the largest number amongst A, B, C and D, what is A? 12. A nine-digit number abcdefghi is such that its digits are all distinct and non-zero. The two-digit number ab is divisible by 2, the three-digit number abc is divisible by 3, the four-digit number abcd is divisible by 4, ...
Binary operations and groups
... multiplication is usually not commutative, in fact (Mn (R), ·), (GLn (R), ·), (SLn (R), ·), (On , ·) are not commutative for n ≥ 2 and (SOn , ·) is not commutative for n ≥ 3. For a set X with #(X) ≥ 2, (X X , ◦) is not commutative, and (SX , ◦) is not commutative for #(X) ≥ 3; in particular (Sn , ◦) ...
... multiplication is usually not commutative, in fact (Mn (R), ·), (GLn (R), ·), (SLn (R), ·), (On , ·) are not commutative for n ≥ 2 and (SOn , ·) is not commutative for n ≥ 3. For a set X with #(X) ≥ 2, (X X , ◦) is not commutative, and (SX , ◦) is not commutative for #(X) ≥ 3; in particular (Sn , ◦) ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.