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COMEDK2017MathematicsComplex Number

If ( 5 + 3 i)³³=2⁴⁹ z , then modulus of the complex number z is equal to

Options

  1. A1
  2. B2
  3. C2 2
  4. D4

Correct answer

B. 2

Step-by-step solution

We have, ( 5 + 3 i)³³=2⁴⁹ z Taking modulus on both sides, we get aligned & .2⁴⁹|z|= 5 + 3 i )³³ & 2⁴⁹|z|=( 5+3 )³³=( 8 )³³=2³³ 2^ 33 / 2 &|z|= 2³³ 2^ 33 / 2 2⁴⁹ =2^ 33 2 -16 =2^ 1 / 2 = 2 aligned

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