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The imaginary unit i is the principal square root of -1, that is, i=sqrt(-1). From this definition, it can also be said that i^2=-1.
Imaginary Unit
i=sqrt(-1) or i^2=-1
The imaginary unit i can also be regarded as a solution to the equation x^2+1=0. x^2+1 = 0 ⇒ i^2+1 = 0 The imaginary unit allows to rewrite the square root of any negative number. Once i replaces the square root of - 1, the square root of the remaining positive number can be evaluated as usual.
sqrt(- a) = sqrt(a) * sqrt(- 1) = sqrt(a) * i
The above property is true only when a>0. Here are some examples of how to use the property to simplify radical expressions. sqrt(-5) &= sqrt(5)* i [0.25em] sqrt(-4) &= sqrt(4)* i = 2i [0.25em] sqrt(-20) &= sqrt(20)* i = sqrt(4* 5)* i = 2sqrt(5)* i The combination of real numbers and any expression of the form bi, with b≠ 0, creates a new set of numbers called imaginary numbers.