The imaginary part of (3+2 √-54)1 / 2-(3-2 √-54)1 / 2 can be

Question

The imaginary part of (3+2 √-54)1 / 2-(3-2 √-54)1 / 2 can be (A) -2 √6 (B) 6 (C) √6 (D) -√6

Tardigrade Admin · Accepted Answer

(3+2 √-54)=3+2 × 3 × √6 i =(3+√6 i )2 (3-2 √54)=(3-√6 i)2 (3+2 √-54)1 / 2+(3-2 √-54)1 / 2 =±(3+√6 i) ±(3-√6 i) =6,-6,2 √6 i ,-2 √6 i , (four possible answer)

Q. The imaginary part of
$(3 + 2 - 54)^{1/2} - (3 - 2 - 54)^{1/2}$ can be

$- 26$

6

$6$

$- 6$

$(3 + 2 - 54) = 3 + 2 \times 3 \times 6 i$
$= (3 + 6 i)^{2}$
$(3 - 254) = (3 - 6 i)^{2}$
$(3 + 2 - 54)^{1/2} + (3 - 2 - 54)^{1/2}$
$= \pm (3 + 6 i) \pm (3 - 6 i)$
$= 6, - 6, 26 i, - 26 i,$ (four possible answer)

Q. The imaginary part of (3+2−54​)1/2−(3−2−54​)1/2 can be

−26​

6

6​

−6​

(3+2−54​)=3+2×3×6​i =(3+6​i)2 (3−254​)=(3−6​i)2 (3+2−54​)1/2+(3−2−54​)1/2 =±(3+6​i)±(3−6​i) =6,−6,26​i,−26​i, (four possible answer)

Q. The imaginary part of
$(3 + 2 - 54)^{1/2} - (3 - 2 - 54)^{1/2}$ can be

$- 26$

$6$

$- 6$

$(3 + 2 - 54) = 3 + 2 \times 3 \times 6 i$
$= (3 + 6 i)^{2}$
$(3 - 254) = (3 - 6 i)^{2}$
$(3 + 2 - 54)^{1/2} + (3 - 2 - 54)^{1/2}$
$= \pm (3 + 6 i) \pm (3 - 6 i)$
$= 6, - 6, 26 i, - 26 i,$ (four possible answer)