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Question 1403a
Complex Numbers
Conjugate Root Theorem
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It is given that
z
1
=
4
+
4
i
{z_1 = 4 + 4 \mathrm{i}}
z
1
=
4
+
4
i
is a root of the equation
z
3
−
11
z
2
+
56
z
−
96
=
0.
z^3 - 11 z^2 + 56 z - 96=0.
z
3
−
11
z
2
+
56
z
−
96
=
0.
The equation has two other roots,
z
2
{z_2}
z
2
and
z
3
,
{z_3,}
z
3
,
where
z
2
{z_2}
z
2
is complex and
z
3
{z_3}
z
3
is real. Find
z
3
.
{z_3.}
z
3
.
Attempt
z
3
=
{z_3 = }
z
3
=
Answer
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