Locate the region in the argand plane for z satisfying |z+i|=|z-2|.

Locate the region in the Argand plane for the complex number z satisfying |z-4| < |z-2|.

Indicate the region in the Argand plane respresented by |z+1|^2+|z-1|^2 =4 .

If log_(sqrt(3))((|z|^(2)-|z|+1)/(2+|z|))>2, then locate the region in the Argand plane which represents z

If A(z_(1)) and B(z_(2)) are two fixed points in the Argand plane the locus of point P(z) satisfying |z-z_(1)|+|z-z_(2)|=|z_(1)-z_(2)| , is

Let z be a complex number in the argand plane wnich satisfies 26|z-3-4i|=|(5+12i)z+(5-12i)bar(z)+13| Then the locus of z is

Locus of z in the argand plane if z satisfies the condition cot^(-1)(log_(3)(|2z+1|))>cot^(-1)(log_(3)(|2z+1|))

The set of points z in the complex plane satisfying |z-i|z||=|z+i|z|| is contained or equal to the set of points z satisfying

Results (1) If P(z) is a variable point and A(z_(1)) and B(z_(2)) are the two fixed points in the argand plane; |z-z_(1)|=|z-z_(2)|

A(z_(1)) and B(z_(2)) are two fixed points in the Argand plane and P(z) is variable point satisfying |z-z_(1)|=k|z-z_(2)| , where k gt 0 and k ne 1 . The locus of is

Consider the region R in the Argand plane described by the complex number. Z satisfying the inequalities |Z-2| le |Z-4| , |Z-3| le |Z+3| , |Z-i| le |Z-3i| , |Z+i| le |Z+3i| Answer the followin questions : Minimum of |Z_(1)-Z_(2)| given that Z_(1) , Z_(2) are any two complex numbers lying in the region R is