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1976 Spain Mathematical Olympiad
5
z^4 + 4(i + 1)z + 1 = 0
z^4 + 4(i + 1)z + 1 = 0
Source: Spanish Mathematical Olympiad 1976 P5
December 23, 2022
complex numbers
algebra
Problem Statement
Show that the equation
z
4
+
4
(
i
+
1
)
z
+
1
=
0
z^4 + 4(i + 1)z + 1 = 0
z
4
+
4
(
i
+
1
)
z
+
1
=
0
has a root in each quadrant of the complex plane.
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