0
Complex Numbers
The square root of negative one, which we now call the imaginary unit, was once thought to be an absurd notion. However, through the diligent studies of open-minded mathematicians, it was shown that the real numbers were actually just one part of a larger set of numbers known as the complex numbers, the other part being the imaginary numbers. Please direct all questions about these surprisingly useful and applicable numbers into this category.
887 Questions
In mathematics, an imaginary number is a number whose square is a negative real number and written in the form bi where i is the imaginary number √(-1) and b is real.
A complex number is a number with both real and imaginary numbers, such as (3+2i), where 3 is real and 2i is imaginary.
Imaginary numbers were 'invented' by Gerolamo Cardano in the 1500's while solving cubic and quartic equations although it is said he did not understand their properties, and they were not properly defined until 1572 by Rafael Bombelli, although he did not name them imaginary numbers.
The name came from Descartes in his book "La Geometrie" where it was meant to be derogatory and sarcastic, as the number √(-1) was thought not to exist by many mathematicians. It was not until the work of Euler in analysis that the imaginary number i was properly understood and widely acknowledged as being a proper number
Another AnswerMathematicians call the horizontal and vertical axes of a graph, the 'real' and 'imaginary' axes. Numbers lying along the real (horizontal) axis are called 'real numbers', and numbers lying along the imaginary (vertical) axis are called 'imaginary numbers'.
(see first discussion page entry)
What is the root of a number called?
The root There is some confusion on the questioner's part. A root is a root.
Numbers have many roots:
The square root of 64 is 8 since 8 squared is 64: 8² = 8 × 8 = 64
The cube root of 64 is 4 since 4 cubed is 64: 4³ = 4 × 4 × 4 = 64
The square root of a number x is sometimes called "radical x" because x appear after the radical (or square root) symbol: √x
As square roots are used a lot, it is also often abbreviated from "square root" to just "root", for example √2 can be read as "root 2" though to be strictly correct it is "square root of 2".
Roots also refer to solutions to equations (linear, quadratics, cubics, or higher polynomials) where they equal 0, for example x = -3 and x = 2 are the roots of the equation x² + x - 6 = 0; x = -2, x = 1 and x = 4 are the roots of x³ - 3x² - 6x + 8 = 0.
The square root of a negative real number is an imaginary number.
We know square root is defined only for positive numbers.
For example,
1) Find the square root of (-1)
It is imaginary. We say that square root of (-1) is i.
In fact they are not real numbers.
2) Find the square root of (-4)
-4 can be written as (-1)(4)
Square root of 4 is 2 and square root of (-1) is i
So, the square root of -4 is 2i.
Similarly, we can find the square root of other negative numbers also.
Source: www.icoachmath.com
An imaginary number is defined to handle square roots of negative numbers. The imaginary unit i is defined as the 'positive' square root of -1.
What are the answers for extra practice lesson 5-4 complex numbers of The McGraw Hill Algebra 2?
I would be haunted by guilt and could never forgive myself if I robbed you of
the opportunity to learn something by working them out on your own. You see,
nobody wants the answers, and nobody needs them. The reason you're given
extra practice is to help you learn something. You've heard of batting practice ?
Putting practice ? Swimming practice ? Band practice ? None of those are done
because the coach needs the practice. They're done by the person who's practicing,
so that he can get good at it. Algebra is exactly the same. If somebody gave you
extra practice, could it possibly be because they thought you need extra practice ?
Hmmm ?
Don't know but look up his grandfather Genghis Khan so look him up and then you can find out about their family history.
Oh, dude, let me break it down for you. So, like, 0.5 is bigger than 0.11 because 0.5 has more tenths than 0.11. It's like comparing a half of a pizza to just a tiny slice. So yeah, 0.5 takes the cake in this math showdown.
What are imaginary numbers of the form a bi and a-bi?
Those are both 'complex' numbers. Together, they are a pair of complex conjugates.
A real number is a rational number that is not imaginary.
5, 3/4, and 8.6 are all real numbers.
3i is not a real number.
Fertilization of the egg by the sperm. The resulting cell is a zygote, which contains the same number of chromosomes as a normal body cell for that species. For example, in humans, sperm cells have 1 set of 23 chromosomes, as do egg cells. So when they unite in fertilization, the zygote will have 2 sets of 23 chromosomes, for a total of 46.
What branches of mathematics are imaginary numbers in?
They are used in many and people who map the earth use complex formulas in map
projections. You can use a formula like (z-1)/(z+i) to bend straight lines into most
anything. See the LINK for an example.
What are complex calculations?
This probably refers to how to handle computations with the set of Complex Numbers (which is a combination of the set of real numbers and imaginary numbers), rather than just complicatedcalculations, or calculations which are very involved and as-such appear very complex (which is a different thing than Complex Numbers).
The division of two complex numbers arithematic operation requires the use of complex conjugate?
(3+2i)/(5+4i)
If you multiply both sides by the conjugate of the denominator (5-4i), you get:
(3+2i)(5-4i)/(5+4i)(5-4i)
= (23-2i)/(25 + 16 +20i - 20i)
= (23-2i)/41
The denominator is now real, because the i terms cancel
As a general formula (easy to expand) this would be:
(a+bi)/(c+di) = [(ac+bd) + (bc-ad)i] / (c^2 + d^2)
It's a very easy method, but if you're the sort of person who loves using general formulas, there it is.
Is every number a complex number?
With math for most people, the set of complex numbers can be considered to enclose all other sets of numbers.
There are, however, sets of numbers that have been created which are outside the scope of 'complex numbers'.
What is the cartesian form of this complex no 1 plus i cube?
(1+i)3 = 1 + 3i - 3 - i
= -2 + 2i
This is a complex number, and therefore cannot be plotted on a Cartesian plane.
If you have a complex function in the form "a+ib", the (complex) conjugate is "a-ib". "Conjugate" is usually a function that the original function must be multiplied by to achieve a real number.
What is the answer to the inequality i313?
Your question makes no sense since i313 is not an inequality.
Try again.
