No, this is not true. ##\sqrt{-5} = i\sqrt{5}## so ##\sqrt{-5} \cdot \sqrt{-5} = i^2 (\sqrt{5})^2 = -5##, not 5 as you show above.Gourav kumar Lakhera said:As we know that √-5×√-5=5
This isn't true, either, for the same reason as above.Gourav kumar Lakhera said:i.e multiplication with it self
My question is that according to this √-1×√-1=1
Gourav kumar Lakhera said:.but it does not hold good in case of i(complex number).
I.e i^2 =-1. Why?
Complex numbers are numbers that contain both a real part and an imaginary part. They are written in the form a + bi, where a is the real part and bi is the imaginary part, with i representing the square root of -1.
Complex numbers are used in various fields of science, including physics, engineering, and mathematics. They are used to represent quantities that have both a magnitude and a direction, such as alternating current in electrical engineering and wave functions in quantum mechanics.
The imaginary unit i is an essential part of complex numbers as it allows us to represent and manipulate quantities that involve the square root of -1. It also helps in solving equations that do not have real solutions.
Yes, complex numbers can be plotted on a graph known as the complex plane. The horizontal axis represents the real part, and the vertical axis represents the imaginary part. This allows for a visual representation of complex numbers and their relationships.
To add complex numbers, we simply add their real and imaginary parts separately. To multiply complex numbers, we use the FOIL method (First, Outer, Inner, Last) or the distributive property. We also use the fact that i squared equals -1 to simplify the result.