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find value of...

Question

find value of x3-ax2+2a2x+4a3 when x/a=1-3i

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Solution

Dear student
$W e h a v e, \frac{x}{a} = 1 - 3 i x = a (1 - 3 i) N o w, x^{3} - a x^{2} + 2 a^{2} x + 4 a^{3} = {(a (1 - 3 i))}^{3} - a {(a (1 - 3 i))}^{2} + 2 a^{2} (a (1 - 3 i)) + 4 a^{3} = a^{3} (1 - 27 i^{3} - 9 i + 27 i^{2}) - a^{3} (1 + 9 i^{2} - 6 i) + 2 a^{3} (1 - 3 i) + 4 a^{3} = a^{3} - 27 a^{3} i - 9 a^{3} i - 27 a^{3} - a^{3} + 9 a^{3} + 6 a^{3} i + 2 a^{3} - 6 a^{3} i + 4 a^{3} = - 12 a^{3} - 36 a^{3} i = - 12 a^{3} (1 - 3 i) = - 12 a^{2} x$
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