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The value of 1 + i2 + i4 + i6 + ... + i40 (where i = √-1) is:1. i2. 03. 14.-1 |
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Answer» Correct Answer - Option 3 : 1 Concept: The imaginary unit i is defined as i = √-1. i4n + 1 = i, i4n + 2 = -1, i4n + 3 = -i, i4n = 1, etc.
Calcultion: The given expression can be written as: i0 + i2 + i4 + i6 + ... + i40 = (i0 + i4 + i8 + ... + i40) + (i2 + i6 + i10 + ... + i38) = [1 + 1 + ... (11 times)] + [-1 + -1 + ... (10 times)] = 11 - 10 = 1. |
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