A, B, C, D are the vertices of a square which are marked in anticlock wise sense. If A(4,4), B(2, 1) then C and D are respectively,
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Answer:
Correct option is
A
B represents the complex number iz
D
D represents the complex number −iz
From the figure, let B be z
2
and D be z
1
.
Since the origin is the center of the square, hence
arg(AB)=
2
π
Therefore, arg(z
2
)−arg(z)=
2
π
arg(z
2
)=
2
π
+arg(z)
Hence, z
2
=∣z∣e
arg(z)+
2
π
=∣z∣.e
arg(z)
.e
2
π
=z.i
=iz
Similarly arg(AD)=
2
−π
Therefore, arg(z
2
)−arg(z)=−
2
π
arg(z
2
)=−
2
π
+arg(z)
Hence, z
2
=∣z∣e
arg(z)−
2
π
=∣z∣.e
arg(z)
.e
−
2
π
=z.(−i)
=−iz
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