If z¹ = 4 - 3 i and z² = - 12 +5i, show that,
(i) z¹+z²—=z¹+z²——
( this is complex numbers chapter. )
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Answered by
1
Answer:
ANSWER
∵∣z
1
∣=∣z
2
∣+∣z
1
+z
2
∣
=∣z
1
∣−∣z
2
∣=∣z
1
+z
2
∣
⇒(∣z
1
∣−∣z
2
∣)
2
=∣z
1
+z
2
∣
2
⇒∣z
1
∣
2
+∣z
2
∣
2
−2∣z
1
∣∣z
2
∣=∣z
1
∣
2
+∣z
2
∣
2
−2∣z
1
∣∣z
2
∣cos(θ
1
−θ
2
)
⇒cos(θ
1
−θ
2
)=1
⇒θ
1
−θ
2
=0
⇒arg(z
1
)−arg(z
2
)=0
⇒
z
2
z
1
is purely real.
⇒lm(
z
2
z
1
)=0.
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