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Question

Let z=(32+i2)5+(32i2)5.
If R(z) and I(z) respectively denote the real and imaginary parts of z, then :
  1. R(z)>0 and I(z)>0
  2. R(z)=3
  3. I(z)=0
  4. R(z)<0 and I(z)>0


Solution

The correct option is C I(z)=0
z=(32+i2)5+(32i2)5   (1)
The equation (1) can be written as
z=(eiπ/6)5+(eiπ/6)5
z=ei5π/6+ei5π/6
z=cos5π6+isin5π6+cos5π6+isin5π6
z=2cos5π6
z=2(32)<0
Im(z)=0 and Re(z)<0

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