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A-level Mathematics/MEI/FP1/Complex Numbers/argand diagram answers
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A-level Mathematics
|
MEI
|
FP1
|
Complex Numbers
1.
z
=
20
+
0
j
{\displaystyle z=20+0j}
wanted form =
z
=
r
(
c
o
s
θ
+
j
s
i
n
θ
)
{\displaystyle z=r(cos\theta +jsin\theta )}
r
=
20
2
+
0
2
=
20
{\displaystyle r={\sqrt {20^{2}+0^{2}}}=20}
t
a
n
(
0
20
)
=
0
{\displaystyle tan({0 \over 20})=0}
z
=
20
(
c
o
s
(
0
)
+
j
s
i
n
(
0
)
)
{\displaystyle z=20(cos(0)+jsin(0))}
2.
z
=
0
+
12
j
{\displaystyle z=0+12j}
wanted form =
z
=
r
(
c
o
s
θ
+
j
s
i
n
θ
)
{\displaystyle z=r(cos\theta +jsin\theta )}
r
=
(
0
2
+
12
2
)
=
12
{\displaystyle r={\sqrt {(}}{0^{2}+12^{2}})=12}
t
a
n
(
12
e
m
0
)
=
∞
{\displaystyle tan({12em \over 0})=\infty }
t
a
n
−
1
(
∞
)
=
π
2
{\displaystyle tan^{-1}(\infty )={\pi \over 2}}
- You need to look at the graph to get this really. Using Sine or Cosine may be advisable in this situation.
z
=
12
(
c
o
s
(
π
2
)
+
j
s
i
n
(
π
2
)
)
{\displaystyle z=12(cos({\pi \over 2})+jsin({\pi \over 2}))}
