√3/2 - √-2/√7 = √3/2-√2(-1)/√7=√3/2-√2i/√7
Answers
Answer:
Complex number: z=x+iy
Modulus: z=
x
2
+y
2
Amplitude: θ=tan
−1
∣
∣
∣
∣
∣
a
b
∣
∣
∣
∣
∣
(i)
z=7−5i
⇒∣z∣=
7
2
+(−5)
2
=8.6
⇒θ=tan
−1
∣
∣
∣
∣
∣
7
−5
∣
∣
∣
∣
∣
=35.53
(ii)
z=
3
+
2
i
⇒∣z∣=
3
2
+
2
2
=2.23
⇒θ=tan
−1
∣
∣
∣
∣
∣
∣
3
2
∣
∣
∣
∣
∣
∣
=39.23)
z=−8+15i
⇒∣z∣=
(−8)
2
+15
2
=17
⇒θ=tan
−1
∣
∣
∣
∣
∣
−8
(15)
∣
∣
∣
∣
∣
=61.92
(iv)
z=−3+3i
⇒∣z∣=
(−3)
2
+3
2
=4.24
⇒θ=tan
−1
∣
∣
∣
∣
∣
3
(−3)
∣
∣
∣
∣
∣
=45
(v)
z=−4−4i
⇒∣z∣=
(−4)
2
+(−4)
2
=5.65
⇒θ=tan
−1
∣
∣
∣
∣
∣
(−4)
(−4)
∣
∣
∣
∣
∣
=45(vii)
z=3+i(0)
⇒∣z∣=
(3)
2
+(0)
2
=3
⇒θ=tan
−1
∣
∣
∣
∣
∣
(3)
(0)
∣
∣
∣
∣
∣
=0
(viii)
z=1+i
⇒∣z∣=
(1)
2
+(1)
2
=1.414
⇒θ=tan
−1
∣
∣
∣
∣
∣
(1)
(1)
∣
∣
∣
∣
∣
=45
(ix)
z=1+
3
i
⇒∣z∣=
(1)
2
+(
3
)
2
=2
⇒θ=tan
−1
∣
∣
∣
∣
∣
∣
(1)
(
3
)
∣
∣
∣
∣
∣
∣
=60
(x)
(1+2i)
2
(1−i)=(−3+4i)(1−i)=−6+7i
z=−6+7i
⇒∣z∣=
(−6)
2
+(7)
2
=2
⇒θ=tan
−1
∣
∣
∣
∣
∣
∣
(−6)
(
7
)
∣
∣
∣
∣
∣
∣
=49.39
Explanation:
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