What are complex numbers, Mathematics

Assignment Help:

Q. What are Complex numbers?

Ans.

Complex numbers are numbers of the form a + bi, where a and b are real numbers and i is a special number called the imaginary unit, which has the property that i = -1. Notice that i is not a real number.

In the complex number a + bi, the first term a is called the real part, and the second term bi is called the imaginary part.

If a complex number has no imaginary part (or, technically speaking, b = 0), then it's real. Otherwise, it's imaginary. A pure imaginary number is a complex number with no real part.

Notice that every real number can be written in the form of a complex number, since (for example) 10 is equal to 10 + 0i.

The big question students always ask is this: if imaginary numbers are "not real", then why are we bothering to talk about them? The truth is this: at one point in history, negative numbers were not considered to "really exist". At one point in history, nobody would believe that not all numbers were rational--and at one point in history, i was considered to be a figment of a warped imagination, which is why it got the name "imaginary".

But nowadays, mathematicians realize that it's OK to make up new kinds of numbers, as long as their mathematical properties are clearly defined. Imaginary numbers are considered to "exist" just as much as real numbers "exist". And they're even useful, tool


Related Discussions:- What are complex numbers

Find the equation to the pair of lines - coordinate geometry, 1. Find the n...

1. Find the number of zeroes of the polynomial y = f(x) whose graph is given in figure. 2 Find the circumcentre of the triangle whose vertices are (-2, -3), (-1, 0) and (7,-6).

Constantinople byzance adrienople nicosia, What was the name of Istanbul be...

What was the name of Istanbul before its capture by the Turks? Constantinople Byzance Adrienople Nicosia

What is the probability in which she gets heads further flip, Jennifer ?ipp...

Jennifer ?ipped a coin three times and got heads each time. What is the probability in which she gets heads on the further ?ip? The probability of heads does not modify based o

Calculate the net amount and distance, 1. A train on the Bay Area Rapid Tra...

1. A train on the Bay Area Rapid Transit system has the ability to accelerate to 80 miles/hour in half a minute. A.   Express the acceleration in miles per hour per minute. B

Find the co ordinates of p such that ap =3/7 ab and p lies, If A & B are (-...

If A & B are (-2,-2) and (2,-4) respectively, find the co ordinates of P such that AP =3/7 AB and P lies on the line segment AB.

Terminology of polynomial, Terminology of polynomial Next we need to ge...

Terminology of polynomial Next we need to get some terminology out of the way. Monomial polynomial A monomial is a polynomial which consists of exactly one term.

Trigonometry, how to change sin 24 degree in digits?

how to change sin 24 degree in digits?

Fractions, what is equizilent to 2/5

what is equizilent to 2/5

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd