1. Tardigrade
  2. Question
  3. Mathematics
  4. The value of i-i2+i3-i4+....-i100 is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. The value of $ i-{{i}^{2}}+{{i}^{3}}-{{i}^{4}}+....-{{i}^{100}} $ is equal to

KEAMKEAM 2011Complex Numbers and Quadratic Equations

Solution:

$ i-{{i}^{2}}+{{i}^{3}}-{{i}^{4}}+...-{{i}^{100}} $
This form a GP with common ratio
$ (r=-1) $ . $ {{S}_{n}}=\frac{i\{1-{{(-i)}^{100}}\}}{1-(-i)} $
$=\frac{i(1-{{i}^{100}})}{1+i} $
$=\frac{i(1-1)}{1+i} $ $ (\because {{i}^{100}}=1) $
$ \therefore $ $ {{S}_{n}}=0 $