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What is complex math?
Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.
The sum of two complex numbers is always a complex number?
A "complex number" is a number of the form a+bi, where a and b are both real numbers and i is the principal square root of -1. Since b can be equal to 0, you see that the real numbers are a subset of the complex numbers. Similarly, since a can be zero, the imaginary numbers are a subset of the complex numbers. So let's take two complex numbers: a+bi and c+di (where a, b, c, and d are real). We add them together and we get: (a+c) + (b+d)i The sum of two real numbers is always real, so a+c is a real number and b+d is a real number, so the sum of two complex numbers is a complex number. What you may really be wondering is whether the sum of two non-real complex numbers can ever be a real number. The answer is yes: (3+2i) + (5-2i) = 8. In fact, the complex numbers form an algebraic field. The sum, difference, product, and quotient of any two complex numbers (except division by 0) is a complex number (keeping in mind the special case that both real and imaginary numbers are a subset of the complex numbers).
How do you muiltiply complex numbers?
If z1=a+ib and z2=c+id then the product z1*z2=(ac-bd)+i(ad+bc)
Is the product of two imaginary numbers always an imaginary number?
If you are talking about pure imaginary numbers (a complex number with no real part) then no. Example: bi times ci where b and c are real numbers equals b*c*i² = b*c*(-1) = -b*c, which is a real number, because b & c & -1 are all real numbers. If you're talking about multiplying two complex numbers (a + bi)*(c + di), then the product will be complex, but it could be real or imaginary, depending on the values of a, b, c, & d.
Are complex numbers under addition and multiplication a field?
The complex numbers are a field.
Can 2 binomials have a monomial product?
No, they cannot with real numbers. With complex numbers it is possible.
What are the similarities between vectors and complex numbers?
If you add two complex numbers, the resulting complex number is equivalent to the vector resulting from adding the two vectors. If you multiply two complex numbers, the resulting complex number is equivalent to the vector resulting from the cross product of the two vectors.
Sets of numbers which has the property that the product of any two numbers in the set is also a number in the set?
Complex numbers, Real numbers, Rational numbers, Integers, Natural Numbers, Multiples of an integer.
What is the difference between real numbers and complex numbers?
Real numbers are a proper subset of complex numbers. In fact each complex number, z, can be represented as z = x +iy where x and y are real numbers and i is the imaginary square root of -1.Thus the set of complex numbers is the Cartesian product of two sets of real numbers. That is, C = R x R where C is the set of complex numbers and R is the set of real numbers. Limitations of this browser prevent me from writing that in a mathematically precise and more helpful fashion.
If the sum of 2 numbers is 4 and the product of these numbers is 13 what are these 2 numbers?
The question has no answer in real numbers. The solution, in complex numbers, are 2+3i and 2-3i where i is the imaginary square root of -1.
What 2 numbers have the product of 7000 and the sum of 55?
The two numbers are the complex conjugate pair27.5 - 79.0174iand27.5 + 79.0174iwhere i is the imaginary square root of -1.
What numbers have the sum of 7 and the product of 70?
The two numbers are the complex conjugate pair, 3.5 - 7.6i and 3.5 + 7.6i where i is the imaginary root of -1
What are the two numbers whose sum is 2 and whose product is -20?
There are no real numbers that satisfy the requirements. The complex solutions are: 1 +/- sqrt(21)
What is the product of a number and its inverse is 1?
That is the identity property of multiplication for all rational numbers, or all real numbers or all complex numbers except (in each case) for 0.
What is complex math?
Complex math covers how to do operations on complex numbers. Complex numbers include real numbers, imaginary numbers, and the combination of real+imaginary numbers.
What is the relation of complex numbers to real numbers?
Complex numbers are a proper superset of real numbers. That is to say, real numbers are a proper subset of complex numbers.
Could anyone list numbers not in the set of complex numbers?
No. Complex numbers is the highest set of numbers you can go, and there are no sets outside of complex numbers.
