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AP EAMCET20228 Jul 2022Evening ShiftMathematicsComplex NumberActual

If (x-i y)^ 1 / 3 =2-i 3 and the point z=(x, y) lies on the line x 2 + y 3 =k , then k=

Options

  1. A16
  2. B2
  3. C8
  4. D4

Correct answer

D. 4

Step-by-step solution

Given, (x-i y)^ 1 / 3 =2-i 3 x-i y=(2-i 3 )^3=8+3 i 3 -i 2 i 3 -18 aligned & x-i y=-10-9 i 3 & x=-10 and y=9 3 aligned Thus, z=x+i y=-10+9 i 3 z lies on the line x 2 + y 3 =k -10 2 + 9 3 3 =k k=4

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