1.

An analytic function f(z) of complex variable z = x + iy may be written as f(z) = u(x, y) + iv(x, y). Then u(x, y) and v(x, y) must satisfy

A. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td><td rowspan="2"> and </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td></tr><tr><td style="text-align: center;"> x</td><td style="text-align: center;"> y</td><td style="text-align: center;"> y</td><td style="text-align: center;"> x</td></tr></table>
B. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td><td rowspan="2"> and </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td></tr><tr><td style="text-align: center;"> x</td><td style="text-align: center;"> y</td><td style="text-align: center;"> y</td><td style="text-align: center;"> x</td></tr></table>
C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td><td rowspan="2"> and </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td></tr><tr><td style="text-align: center;"> x</td><td style="text-align: center;"> y</td><td style="text-align: center;"> y</td><td style="text-align: center;"> x</td></tr></table>
D. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td><td rowspan="2"> and </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td></tr><tr><td style="text-align: center;"> x</td><td style="text-align: center;"> y</td><td style="text-align: center;"> y</td><td style="text-align: center;"> x</td></tr></table>
Answer» C. <table><tr><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td><td rowspan="2"> and </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> u</center></td><td rowspan="2"> = - </td><td style="border-bottom:1px solid #000000;vertical-align:bottom;padding-bottom:2px;"><center> v</center></td></tr><tr><td style="text-align: center;"> x</td><td style="text-align: center;"> y</td><td style="text-align: center;"> y</td><td style="text-align: center;"> x</td></tr></table>


Discussion

No Comment Found

Related MCQs