Complex Variables and Partial Differential Equations (3130005)

Question-1c ( ii )

BE | Semester-3 Summer-2020 | 27-10-2020

Q1) (c ( ii ))

Find the real and imaginary parts of $f (z) = z^{2} + 3 z$ .

f (z) = z^{2} + 3 z

\Rightarrow f (z) = {(x + iy)}^{2} + 3 (x + iy)

\Rightarrow f (z) = x^{2} + 2 ixy - y^{2} + 3 x + 3 iy

\Rightarrow f (z) = (x^{2} - y^{2} + 3 x) + i (3 y + 2 xy)

\Rightarrow Re [f (z)] = (x^{2} - y^{2} + 3 x) & Im [f (z)] = (3 y + 2 xy)

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