Consider the function f(z)=z+z∗ where z is a complex variable and z∗ denotes its complex conjugate.Which oneof the following is TRUE?
A
f(z) is both continuous and analytic
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B
f(z) is a continuous but not analytic
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C
f(z) is not continuous but is analytic
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D
f(z) is neither continuous nor analytic
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Solution
The correct option is Bf(z) is a continuous but not analytic z=x+iy & z∗=x−iy
Then f(z)=z+z∗=2x ∵f(z) is in polynomial form hence continuous
Again f(z)=2x=u+iv ⇒u=2x & v=0 ∵CR equation are not satisfied throughout the domain of f(z) hence not analytic.