JEE MAIN - Mathematics (2019 - 11th January Morning Slot - No. 19)
Let $${\left( { - 2 - {1 \over 3}i} \right)^3} = {{x + iy} \over {27}}\left( {i = \sqrt { - 1} } \right),\,\,$$ where x and y are real numbers, then y $$-$$ x equals :
$$-$$ 85
85
$$-$$ 91
91
Explanation
$${\left( { - 2 - {i \over 3}} \right)^3} = - {{{{\left( {6 + i} \right)}^3}} \over {27}}$$
$$ = {{ - 198 - 107i} \over {27}} = {{x + iy} \over {27}}$$
Hence, $$y - x = 198 - 107 = 91$$
$$ = {{ - 198 - 107i} \over {27}} = {{x + iy} \over {27}}$$
Hence, $$y - x = 198 - 107 = 91$$
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