Question

Z-Zbar=0 if and only if (a)Re(z)=0 (b)Im(z)=0 (c)z=0 (d) none of them​

Answer 1

Answer:

option B

Step-by-step explanation:

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Answer 2

Answer:

Option(b) is correct.

If Z-Zbar = 0 then Im(Z) = 0

Step-by-step explanation:

Complex number:

• Complex number are the numbers which consists of two parts- a real part and an imaginary part.
• The set of all complex numbers is denoted by C.
• Complex number is written in the form of x+iy, where x is the real part and iy is the imaginary part.          

Properties of complex number:

• The properties of complex number and its conjugate number is always a real number.
• The complex number that is given is the result of obtaining the conjugate for conjugate of any complex number.
• If the conjugate of the complex number is the same complex number then the imaginary part will be zero.  
• Sum of a complex number and its conjugate is equal to 2 times the real part of the complex number.
• Difference of a complex number and its conjugate is equal to 2i times the imaginary part of the complex number.

Given Z-Zbar = 0

      we know Z = x+iy is a complex number

                Zbar = x-iy is the conjugate of Z.

                     Z-Zbar = 0

                x+iy-(x-iy) = 0

                x+iy-x+iy = 0    

                     2iy = 0

                     (2y)i = 0

                  Im(Z) = 0

               Hence, Im(Z) = 0

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