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4 sie 2015 · A non-real, or imaginary, number is any number that, when multiplied by itself, produces a negative number. Mathematicians use the letter “i” to symbolize the square root of -1. An imaginary number is any real number multiplied by i. For example, 5i is imaginary; the square of 5i is -25.
A complex number consists of a “real” part and an “imaginary” (non-real) part, and typically looks like $ a+bi$, where “$ a$” is the real part, and “$ b$” is the imaginary part, following by “$ i$”, to indicate the “imaginary” unit.
An imaginary number is the product of a real number and the imaginary unit i, [note 1] which is defined by its property i2 = −1. [1][2] The square of an imaginary number bi is −b2. For example, 5i is an imaginary number, and its square is −25. The number zero is considered to be both real and imaginary. [3]
Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with real or complex coefficients has a solution which is a complex number.
Imaginary numbers are numbers that are not real. We know that the quadratic equation is of the form ax 2 + bx + c = 0, where the discriminant is b 2 – 4ac. Whenever the discriminant is less than 0, finding square root becomes necessary for us.
9 kwi 2015 · A number which is imaginary, is NOT a real number. All real numbers can be expressed on the number line, while imaginary numbers cannot be expressed on the number line
z is a Complex Number; a and b are Real Numbers; i is the unit imaginary number = √−1; we refer to the real part and imaginary part using Re and Im like this: Re(z) = a Im(z) = b. The conjugate (it changes the sign in the middle) of z is shown with a star: z * = a − bi. We can also use angle and distance like this (called polar form):
