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AP EAMCET2010MathematicsComplex Number

If z=1+i 3 then | Arg z|+| Arg z | is equal to

Options

  1. A0
  2. B3
  3. C2
  4. D2 3

Correct answer

D. 2 3

Step-by-step solution

z=1+i 3 Let 1+i 3 =r( +i ) Then, r =1 (i) r = 3 (ii) Eq. (i) + Eq. (ii), we get r^2 ( ^2 + ^2 )=3+1 ( ^2 + ^2 =1 )r^2=4r=2 Eq. (ii) Eq. (i), we get = 3 = 3 = 3 So, z=(1+i 3 )=2 3 +i 3 Then z =(1-i 3 )=2 3 -i 3 =2 ( - 3 )+i ( - 3 ) So, Arg z= 3 Arg z =- 3 | Arg z|+| Arg z |= | 3 |+ | - 3 |= 3 + 3 = 2 3

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