Question
Download Solution PDFThe complex number \({{\left( \frac{2+i}{3-i} \right)}^{2}}\) is
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven complex no. \({{\left( \frac{2+i}{3-i} \right)}^{2}}\)
\(z={{\left( \frac{2+i}{3-i} \right)}^{2}}=\frac{4-1+4i}{9-1-6i}=\frac{3+4i}{8-6i}\)
Rationalize the above expression
\(z=\frac{\left( 3+4i \right)}{\left( 8-6i \right)}\frac{\left( 8+6i \right)}{\left( 8+6i \right)}=\frac{\left( 24+32i+18i-24 \right)}{64+36}=\frac{50i}{100}=\frac{i}{2}\)
\(\Rightarrow z=\frac{i}{2}=\frac{1}{2}~\left[ \cos \frac{\pi }{2}+i\sin \frac{\pi }{2} \right]\)Last updated on May 28, 2025
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