A complex number consists of a real part and an "imaginary" part and has the from a + bi where a and b are real numbers and i is a mathematical symbol which is called the imaginary unit.
The imaginary unit "i" is â-1 so in that sense, a complex number can only come out where there is a term involving the root of a negative number. However, complex numbers appear in many fields, including engineering, electromagnetism, quantum physics, applied mathematics, and chaos theory.
They come up in other contexts where functions are not defined over the reals. For example, you can't take the log of a negative number, but ln(-1) = iÏ. Also, arcsin(2) is expressible in terms of i.
They can come out in lots of other contexts. For example, frequency analysis, control theory, improper integrals, quantum mechanics, special and general relativity, dynamic differential equations, and many other areas.
Not really the very definition of an imaginary number is the sqrt(negative number). They do pop up in various places, but always as sqrt(negative number)
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square root of a negative no. was the reason for which complex nos came into picture. So i think this is the only way we can have complex nos!!!
A complex number consists of a real part and an "imaginary" part and has the from a + bi where a and b are real numbers and i is a mathematical symbol which is called the imaginary unit.
The imaginary unit "i" is â-1 so in that sense, a complex number can only come out where there is a term involving the root of a negative number. However, complex numbers appear in many fields, including engineering, electromagnetism, quantum physics, applied mathematics, and chaos theory.
Yes. Complex numbers are of the form a + bi where i is the sqrt(-1). From this we have:
i^(2) = (-1) and sqrt(-x) = sqrt(x)i
So as you can see any mathematical manipulation that generates sqrt(-1) generates a complex number at some stage.
They come up in other contexts where functions are not defined over the reals. For example, you can't take the log of a negative number, but ln(-1) = iÏ. Also, arcsin(2) is expressible in terms of i.
They can come out in lots of other contexts. For example, frequency analysis, control theory, improper integrals, quantum mechanics, special and general relativity, dynamic differential equations, and many other areas.
Not really the very definition of an imaginary number is the sqrt(negative number). They do pop up in various places, but always as sqrt(negative number)