Is there an easier way to solve the

Andreas Gallegos

Andreas Gallegos

Answered question

2022-04-14

Is there an easier way to solve the given problem?
If x+2+3i=0 then find the value of 2x4+3x3x215x+36.

Answer & Explanation

fallendreamsit2p

fallendreamsit2p

Beginner2022-04-15Added 14 answers

Real coefficients in the quartic inspired me to multiply x+2+3i; by the conjugate, which gives
(x+2+3i)(x+23i)=x2+4x+7.
Dividing the given expression by x2+4x+7 (just to see if we get a simple form) leads to
2x4+3x3x215x+36=(x2+4x+7)0(2x25x+5)+1
Yes, if x+2+3i=0; then
2x4+3x3x215x+36=1.

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