Complex Variables and Partial Differential Equations (3130005)

Question-1a

BE | Semester-3 Winter-2019 | 26-11-2019

Q1) (a)

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

f (z) = \frac{3 i}{2 + 3 i}

\Rightarrow f (z) = \frac{3 i}{2 + 3 i} \times \frac{2 - 3 i}{2 - 3 i}

\Rightarrow f (z) = \frac{6 i - 9 i^{2}}{2^{2} - 3^{2} i^{2}}

\Rightarrow f (z) = \frac{6 i + 9}{4 + 9}

\Rightarrow f (z) = \frac{9 + 6 i}{13}

\Rightarrow f (z) = \frac{9}{13} + \frac{6 i}{13}

\Rightarrow Re (f (z)) = \frac{9}{13} & Im (f (z)) = \frac{6}{13}

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