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TS EAMCET · Maths · Complex Number

If the roots of the equation (z-4)3=8i are a-2i, b+i, and c+i, then abc=

  1. A 133
  2. B 413
  3. C 213
  4. D 53
Verified Solution

Answer & Solution

Correct Answer

(C) 213

Step-by-step Solution

Detailed explanation

Given, the roots of z-43=8i are a-2i, b+i and c+i. Let z=x+iy, then x+iy-43=8i ⇒x-4+iy3=8i ⇒x-43+iy3+3x-42iy+3x-4iy2=8i Using i2=-1, i3=-i, ⇒x-43-iy3+3x-42iy-3x-4y2=8i On comparing the real and imaginary parts on both sides of the equation, we get…