Let [( - 2 - 1 3i )^3 = x + iy 27( i = - 1 ),,,] where x and y are real numbers, then y - …

Question

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 :

Accepted Answer

$${\left( { - 2 - {i \over 3}} \right)^3} =  - {{{{\left( {6 + i} \right)}^3}} \over {27}}$$

$$ = {{ - 198 - 107i} \over {27}} = {{x + iy} \over {27}}$$

Hence,  $y - x = 198 - 107 = 91$

Solutions · 1