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KCET2007MathematicsComplex Number

The amplitude of (1+i)⁵ is

Options

  1. A3 4
  2. B-3 4
  3. C-5 4
  4. D5 4

Correct answer

D. 5 4

Step-by-step solution

Given, (1+i)⁵ aligned &=( 2 )⁵ ( 1 2 + i 2 )⁵ &=( 2 )⁵ ( 4 +i 4 )⁵ &=( 2 )⁵ ( 5 4 +i 5 4 ) aligned [by De-Moivre's theorem] Now, amplitude = ⁻¹ ( y x ) = ⁻¹ ( 5 4 5 4 )= 5 4

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