AP EAMCET · Maths · Complex Number
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 \(\widehat{\mathrm{Z}_1 \mathrm{Z}_2}=\)
- A \(\hat{Z}_1 \hat{Z}_2\)
- B \(\hat{Z}_1 \hat{\bar{Z}}_2\)
- C \(\bar{Z}_1 \hat{Z}_2\)
- D \(\hat{z}_1 Z_2\)
Answer & Solution
Correct Answer
(C) \(\bar{Z}_1 \hat{Z}_2\)
Step-by-step Solution
Detailed explanation
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.
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