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KCET2013MathematicsComplex Number

The modulus and amplitude of 1+2 i 1-(1-i)² are

Options

  1. A2 and 6
  2. B1 and 4
  3. C1 and 0
  4. D1 and 3

Correct answer

C. 1 and 0

Step-by-step solution

Let z= 1+2 i 1-(1-i)² z= 1+2 i 1- (1+i²-2 i ) = 1+2 i -i²+2 i = 1+2 i 1+2 i ( i²=-1 ) z=1+0 i Modulus of z=|z|=|1+0 i|= 1²+0² =1 and amplitude of z ⁻¹ ( 0 1 )= ⁻¹(0)= ⁻¹( 0)=0

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