Q25 of 66 Page 91

Fill in the blanks of the following

If then the locus of z is ………….

Explanation:


Given




⇒ 6 |x – 2 + iy| = π |x + 2 + iy|


Squaring on both sides,


⇒ 36 |x – 2 + iy|2 = π2 |x + 2 + iy|2


⇒ 36 [x2 – 4x + 4 + y2] = π2 [x2 – 4x + 4 + y2]


⇒ (36 – π2) x2 + (36 – π2) y2 – (144 + 4π2) x + 144 – 4π2 = 0


Which is a circle.


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25

Fill in the blanks of the following

arg (z) + arg is …………….

 25

Fill in the blanks of the following

If |z + 4| ≤ 3, then the greatest and least values of |z + 1| are ……… and …….

 25

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If |z| = 4 and arg (z) = 5π/6, then z = ………..

 26

State True of False for the following:

The order relation is defined on the set of complex numbers.