For a complex number \(Z=a+i b\), let \(\hat{\mathrm{Z}}\) \(=b+i a\). If \(Z_1, Z_2\) are such complex…
For a complex number \(Z=a+i b\), let \(\hat{\mathrm{Z}}\) \(=b+i a\). If \(Z_1, Z_2\) are such complex numbers, then \(\widehat{\mathrm{Z}_1 \mathrm{Z}_2}=\)
\(\hat{Z}_1 \hat{Z}_2\)
\(\hat{Z}_1 \hat{\bar{Z}}_2\)
\(\bar{Z}_1 \hat{Z}_2\)
\(\hat{z}_1 Z_2\)
Solution
For given complex number \(Z=a+i b\), it is given that \(\hat{Z}=b+i a\)
Let \(Z_1=a+i b\) and \(Z_2=c+i d\)
Then, \(Z_1 Z_2=(a c-b d)+i(a d+c b)\)
Hence, option (c) is correct.