divide 2x⁴+5x³+7x²+x+2 by x²+1
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2x
4
+5x
3
+4x
2
−x+41 ---(1)
when x=−2−
3
i=−(2+
3
i)---(2)
x
2
=(2+
3
i)
2
=4+3(i)
2
+4
3
i
=4−3+4
3
! (∵i
2
=−1)
x
2
=1+4
3
i ---(3)
x
3
=x
2
.x
=(1+4
3
i)[−(2+
3
i)]
=−(2+
3
i+8
3
i+12!
2
)
=−(2−12+9
3
i)
x
3
=10−9
3
i ---(4)
x
4
=(x
2
)
2
=(1+4
3
i)
2
=1+48!
2
+8i
3
=1−48+8i
3
(i
2
=−1)
x
4
=−47+8!
3
---(5)
From (1),(2),(3),(4) and (5)
2(−47+8i
3
)+5(10−9
3
i)+7(1+4
3
i)−(−2
3
i)+41 −94+16i
3
+50−45
3
i+7+28
3
i+2+
3
i+41
=6 d)
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