root 2 (7pi/4 + i sin 7pi/4)
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1
Answer:
A complex number of form
r
cos
θ
+
i
r
sin
θ
can also be written as
r
⋅
e
i
θ
.
Hence,
z
1
=
√
2
(
cos
(
7
π
4
)
+
i
sin
(
7
π
4
)
)
=
√
2
e
i
7
π
4
and
z
2
=
2
(
cos
(
5
π
3
)
+
i
sin
(
5
π
2
)
)
=
2
e
i
5
π
3
Hence
z
1
z
2
=
√
2
2
x
e
i
(
7
π
4
−
5
π
3
)
=
1
√
2
⋅
e
i
(
21
π
−
20
π
12
)
=
1
√
2
⋅
e
i
π
12
=
1
√
2
[
cos
(
π
12
)
+
i
sin
(
π
12
)
]
Step-by-step explanation:
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