write the polar form of 2-2i
Answers
Answered by
0
Step-by-step explanation:
That is
(
x
,
y
)
→
(
r
,
θ
)
Reminder
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
a
a
r
=
√
x
2
+
y
2
a
a
∣
∣
∣
−−−−−−−−−−−−−−−−−
and
∣
∣
∣
∣
¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯
a
a
θ
=
tan
−
1
(
y
x
)
a
a
∣
∣
−−−−−−−−−−−−−−−−−−
here x = 2 and y = -2
⇒
r
=
√
2
2
+
(
−
2
)
2
=
√
8
=
2
√
2
Now 2 - 2i is in the 4th quadrant, hence we must ensure that
θ
is in the 4th quadrant.
θ
=
tan
−
1
(
−
2
2
)
=
tan
−
1
(
−
1
)
=
−
π
4
in 4th quadrant
⇒
2
−
2
i
=
(
2
,
−
2
)
→
(
2
√
2
,
−
π
4
)
Answered by
0
Answer:( 2 , − 2 ) → ( 2 √ 2 , − π 4 )
Step-by-step explanation:
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