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(b)
P.M./Complex/p.6
imaginary axis
z1 = x1 + iy 1 and z 2 = x2 + iy 2
z1 - z2 = (x1 - x2 ) + i(y1 - y2 )
z1 - z2 =
C
(x1 - x2 )2 + (y1 - y2 )2
B
= the distance between the points
A
representing z1 and z 2
3.
0
real axis
∴
A, B and C form an equilateral △
iff
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iff
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iff
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iff
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iff
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In the Argand diagram, PQR is an equilateral △ whose circumcentre is at the origin. If P represents
the complex number 4 + i, find the complex numbers represented by Q and R.
Solution :
imaginary axis
By definition,
∠POQ = ∠QOR = ∠ROP = __________
4 + i = 17 e i
the complex number represented by Q
= ____________________________________________
P(4,1)
Q
0
real
axis
= ____________________________________________
= ____________________________________________
= ____________________________________________
R
the complex number represented by R
= ____________________________________________
= ____________________________________________
= ____________________________________________
Classwork (99 II Q.5)
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