Express the following in modulus and neighbourhood form
(1) 3.8 < x < 4.8
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Answer:
Answer
1−3i
1+2i
1−3i
1+2i
×
1+3i
1+3i
1
2
−(3i)
2
(1+2i)(1+3i)
1−(−9)
1+2i+3i+6i
2
10
−5+5i
2
−1+i
∴z=−
2
1
+i
2
1
arg(z)=
a
2
+b
2
=
(
2
−1
)
2
+(
2
1
)
2
∴arg(z)=
2
1
r
2
=a
2
+b
2
⇒r
2
=(
2
−1
)
2
+(
2
1
)
2
∴r=
2
1
θ=tan
−1
(
a
b
)+180
∘
∵a<0
∴θ=tan
−1
(
2
1
2
−1
)+180
∘
θ=−45
∘
+180
∘
=135
∘
=
4
3π
∴z=r(cosθ+sinθ)
z=
2
1
(cos
4
3π
+sin
4
3π
)
Explanation:
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