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KCET2011MathematicsComplex Number

The value of 1+i 3 (1+ 1 i+1 )² is

Options

  1. A20
  2. B9
  3. C5 4
  4. D4 5

Correct answer

D. 4 5

Step-by-step solution

| 1+i 3 (1+ 1 i+1 )² |= | (1+i 3 )(i+1)² (i+2)² | ( i²=-1 )= | (1+i 3 ) (i²+1+2 i ) (i²+4+4 i ) |= | (1+i 3 ) 2 i (4 i+3) |= | -2 3 +2 i 3+4 i |=2 | (- 3 +i)(3-4 i) (3+4 i)(3-4 i) |=2 | -3 3 +3 i+4 3 i+4 25 |= 2 25 |(4-3 3 )+(3+4 3 ) i|= 2 25 (4-3 3 )²+(3+4 3 )² = 2 25 16+27-24 3 +9+48+24 3 = 2 25 100 = 2 10 25 = 4 5

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