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AP EAMCET2004MathematicsComplex Number

The value of _ n=0 ^ ( 2 i 3 )^n is

Options

  1. A9+6 i 13
  2. B9-6 i 13
  3. C9+6 i
  4. D9-6 i

Correct answer

A. 9+6 i 13

Step-by-step solution

aligned & _ n=0 ^x ( 2 i 3 )^n &=1+ ( 2 i 3 )+ ( 2 i 3 )^2+ ( 2 i 3 )^3+ . &= 1 1- 2 i 3 = 3 3-2 i 3+2 i 3+2 i aligned

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