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Mathematics
Mathematics
Problem
Let
r
r
r
and
θ
\theta
θ
respectively be the modulus and amplitude of the complex number
z
=
2
−
i
(
2
tan
5
π
8
)
z = 2 - i \left( 2 \tan \frac{5\pi}{8} \right)
z
=
2
−
i
(
2
tan
8
5
π
)
, then
(
r
,
θ
)
(r, \theta)
(
r
,
θ
)
is equal to [Jan. 29, 2024 (II)] (a)
(
2
sec
11
π
8
,
11
π
8
)
\left( 2 \sec \frac{11\pi}{8}, \frac{11\pi}{8} \right)
(
2
sec
8
11
π
,
8
11
π
)
(b)
(
2
sec
5
π
8
,
3
π
8
)
\left( 2 \sec \frac{5\pi}{8}, \frac{3\pi}{8} \right)
(
2
sec
8
5
π
,
8
3
π
)
(c)
(
2
sec
3
π
8
,
5
π
8
)
\left( 2 \sec \frac{3\pi}{8}, \frac{5\pi}{8} \right)
(
2
sec
8
3
π
,
8
5
π
)
(d)
(
2
sec
3
π
8
,
3
π
8
)
\left( 2 \sec \frac{3\pi}{8}, \frac{3\pi}{8} \right)
(
2
sec
8
3
π
,
8
3
π
)
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