Question

The sum of i - 2 - 3i + 4 + ....... upto 100 terms, which i = $\sqrt{-1}$

is

• A. 50(1-i)
• B. 25i
• C. 25(1+i)
• D. 100(1-i)

Answer 1

The correct option is A

50(1-i)

Let S = i - 2 - 3i + 4 + 5i + ....... + 100 $i^{100}$

⇒ S = i + 2$i^2$ + 3 $i^3$ + 4 $i^4$ + 5$i^5$ + ........ + 100 $i^{100}$

⇒iS = $i^2$ + 2$i^3$ + 3 $i^4$ + 4 $i^5$ + ........ + 99$i^{100}$ + 100 $i^{101}$

∴ S - iS = [i + $i^2$ + $i^3$ + $i^4$ +.........+$i^{100}$] - 100 $i^{101}$

⇒S(1 - i) = 0 - 100$i^{101}$ = -100i

∴ S = $\frac{-100i}{1-i}$ = -50i(1 + i) = -50(i - 1) = 50(1 - i).