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Imaginary numbers are based on the mathematical number i i. i is defined to be −1−−−√ i is defined to be − 1. From this 1 fact, we can derive a general formula for powers of i i by looking at some examples. Table 1. Table 1 Expression i2 i3 i4 = = = Work i ⋅ i = −1−−−√ ⋅ −1−−−√ i2 ⋅ i = −1 ⋅ i i2 ⋅ i2.
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Imaginary Numbers An Imaginary Number, when squared, gives a negative result. Try Let's try squaring some numbers to see if we can get a negative result: 2 × 2 = 4 (−2) × (−2) = 4 (because a negative times a negative gives a positive) 0 × 0 = 0 0.1 × 0.1 = 0.01 No luck! Always positive, or zero.
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An imaginary number is obtained by taking the square root of a negative integer. Value of i = √-1. In order to grasp the principles of complex numbers, we utilize this value of i. In the case of a quadratic equation , x 2 + 1 = 0. x 2 = - 1. x = √-1. Here, √-1 is the imaginary part. i = √-1.
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The number i is by no means alone! By taking multiples of this imaginary unit, we can create infinitely many more pure imaginary numbers. For example, 3 i , i 5 , and − 12 i are all examples of pure imaginary numbers, or numbers of the form b i , where b is a nonzero real number.
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An imaginary number is a real number multiplied by 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]
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