1.

The value of 1 + i2 + i4 + i6 + ... + i40 (where i = √-1) is:1. i2. 03. 14.-1

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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