Find two imaginary numbers whose sum is a real number. How are the imaginary numbers related?

Answer 1

Actually, the answer is not a conjugate pair. A conjugate pair consists of one real part and one imaginary part, which is completely different from an imaginary number. An imaginary number is a single term with the function "i" within it. Example s of functions are i, 2i, -3i, 5/4 i, and -9i.

The two imaginary numbers that add up to a real number would be i and -i, because i + (-i) = i - i = 0. Thus, the two imaginary numbers become a real number, 0.

(Just as a note, an equation in the form a + bi is called a complex number, not an imaginary.)

Answer 2

Imaginary number

In mathematics, an imaginary number (or purely imaginary number) is a complex number whose squared value is a real number not greater than zero. The imaginary unit, denoted by or is an example of an imaginary number. If y is a real number, then i•y is also an imaginary number, because:


Imaginary numbers were defined in 1572 by Rafael Bombelli. At the time, such numbers were thought not to exist, much as zero and the negative numbers were regarded by some as fictitious or useless. Many other mathematicians were slow to believe in imaginary numbers at first, including Descartes who wrote about them in his La Géométrie, where the term was meant to be derogatory.[1]


Although Descartes originally used the term imaginary number to mean what is currently meant by the term complex number, the term imaginary number today usually means a complex number with a real part equal to 0, that is, a number of the form i•y. Zero (0) is the only number that is both real and imaginary.



Real number definition


In mathematics, the real numbers may be described informally as numbers that can be given by an infinite decimal representation, such as 2.4871773339…. The real numbers include both rational numbers, such as 42 and −23/129, and irrational numbers, such as π and the square root of 2, and can be represented as points along an infinitely long number line.

A more rigorous definition of the real numbers was one of the most important developments of 19th century mathematics. Popular definitions in use today include equivalence classes of Cauchy sequences of rational numbers, Dedekind cuts, a more sophisticated version of "decimal representation", and an axiomatic definition of the real numbers as the unique complete Archimedean ordered field.

The name real numbers arose to distinguish them from what was then called imaginary numbers (and now complex numbers).

Descartes postulated that Imaginary Numbers are Complex Numbers, and Dedekind Further Postulated that both Complex and Real Numbers could be plotted on an indefinate number line:
The Hypothesis is that currently math scollars agree: Real Numbers, Imaginary Numbers and Complex Numbers are all names for the same group of numbers.

This is a kind of a trick question
Any 2 Imaginary Numbers when combimed make a real number, The immaginary numbers are related as they can all be plotted on a number line.

This is the kind of question you get when your math teacher gets bored or begins to believe he's the greatest math scollar ever.

Ask the teacher why he thaught this was an importand question to ask.

Ask him to supply his version of the correct responce to the question on this cite for review by his piers

Answer 3

the way you have worded the question seems to rule out a
real and imaginary number

So the only two numbers are +i and -i which when added gives zero

Answer 4

, think of two complex numbers written in a general form:

a+bi
c+di

where a, b, c, d are numbers

if you add these two complex numbers, you get

(a+c)+i(b+d) if b=-d, there is no imaginary part, and you get a real number

this means the numbers are written as a+ib and c-ib

Answer 5

The numbers are called conjigates (I may have spelled that wrong.) where the imaginary numbers have equal magnatudes but opposite signs for example

3+4i and 3-4i

Answer 6

Let a+bi be any complex number.
Then a+ bi + a-bi = 2a, which is real.
A complex number and its conjugate always
sum to a real number.

Answer 7

they are conjugates

Answer 8

u+iv, x-iv