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Dividing by , where , weobtain the remainder and dividing it by , we get the…
MATHEMATICS · Subjective · CBSE · Mathematics · Polynomials · Polynomials
Problem
Dividing
f
(
z
)
f(z)
f
(
z
)
by
z
−
i
z - i
z
−
i
, where
i
=
−
1
i = \sqrt{-1}
i
=
−
1
, weobtain the remainder
i
i
i
and dividing it by
z
+
i
z + i
z
+
i
, we get the remainder
1
+
i
1 + i
1
+
i
. Find the remainder upon the division of
f
(
z
)
f(z)
f
(
z
)
by
z
2
+
1
z^2 + 1
z
2
+
1
.
Related theory
Algebra of Complex Numbers
Complex Numbers
Division Algorithm for Polynomials
Polynomials
Complex Number Operations
Algebra
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