JEE PYQ: Complex Numbers Question 15
Question 15 - 2020 (02 Sep Shift 2)
The imaginary part of $(3+2\sqrt{-54})^{1/2} - (3-2\sqrt{-54})^{1/2}$ can be:
(1) $-\sqrt{6}$
(2) $-2\sqrt{6}$
(3) $6$
(4) $\sqrt{6}$
Show Answer
Answer: (2)
Solution
$3 + 2\sqrt{-54} = 3 + 6i\sqrt{6}$. Let $(a+bi)^2 = 3 + 6i\sqrt{6}$: $a^2 - b^2 = 3$, $2ab = 6\sqrt{6}$. Solving: $a = 3, b = \sqrt{6}$. Similarly for the conjugate. Imaginary part of difference $= 2\sqrt{6}$ or $-2\sqrt{6}$.
BETA
