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Question 1420b
Complex Numbers
2020 Paper 1 Question 6 Variant
Question
Generate new
The complex number
z
{z}
z
satisfies the equation
z
2
(
4
+
2
i
)
+
(
−
5
−
19
i
)
z
+
t
=
0
,
z^2(4 + 2 \mathrm{i}) + (- 5 - 19 \mathrm{i})z + t = 0,
z
2
(
4
+
2
i
)
+
(
−
5
−
19
i
)
z
+
t
=
0
,
where
t
{t}
t
is a real number. It is given that one root is of the form
k
+
k
i
,
{k + k \mathrm{i},}
k
+
k
i
,
where
k
{k}
k
is real and non-zero.
Find
t
{t}
t
and
k
,
{k,}
k
,
and the other root of the equation.
[8]
Answer
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