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Simplification of an Expression

Find the valu...

Question

Find the value of $x^{4} - x^{3} + x^{2} + 3 x - 5$ if x = 2+3i

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Solution

$x^{4} - x^{3} + x^{2} + 3 x - 5$

${(2 + 3 i)}^{4} - {(2 + 3 i)}^{3} + {(2 + 3 i)}^{2} + 3 (2 + 3 i) - 5$

${(2 + 3 i)}^{4} : - 119 - 120 i$

${(2 + 3 i)}^{3} : - 46 + 9 i$

${(2 + 3 i)}^{2} : - 5 + 12 i$

$= (- 119 - 120 i) + 46 - 9 i + (- 5 + 12 i) + 6 + 9 i - 5$

$= - 119 - 120 i + 46 - 9 i - 5 + 12 i + 6 + 9 i - 5$

$= - 120 i - 9 i + 12 i + 9 i - 119 + 46 - 5 + 6 - 5$

$= - 108 i - 119 + 46 - 5 + 6 - 5$

$= - 77 - 108 i$

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Similar questions

x = 2 + 3 i

, then the value of

x^{4} - x^{3} + 10 x^{2} + 3 x - 5

g (x) = x^{4} {- x}^{3} + x^{2} + 3 x - 5

g (2 + 3 i)

g (x) = x^{4} - x^{3} \div x^{2} + 3 x - 5

g (2 + 3 i)

(i) Find the real values of

x

y

z_{1} = 9 y^{2} - 4 - 10 i x

is complex conjugate of each other.

(ii) Find the value of

x^{4} - x^{3} + x^{2} + 3 x - 5

x = 2 + 3 i

g (x) = x^{4} - x^{3} + x^{2} + 3 x - 5

, then the value of

g (2 + 3 i)

- K - 108 i

K

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Simplification of an Expression

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