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COMPLEX NUMBERS | STANDARD LOCI IN THE ARGAND PLANE, SQUARE ROO OF A COMPLEX NUMBERS | If P(z) is a variable point and `A(z_1)and B(z_2)` are the two fixed points in the argand plane, and `|z-z_1|=|z-z_2|`, then what is the locus of z?, 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|^2+|z-z_2|^2=|z_1-z_2|^2`, then find locus of z., If P(z) is a variable point and `A(z_1)and B(z_2)` are the two fixed points in the argand plane `arg((z-z_1)/(z-z_2))=alpha` (fixed), then find locus of z., If P(z) is a variable point and `A(z_1)and B(z_2)` are the two fixed points in the argand plane (i)`arg((z-z_1)/(z-z_2))=pmpi/2 ` (ii) `arg((z-z_1)/(z-z_2))=0 or pi`, then find the locus of z?, If P(z) is a variable point and `A(z_1)and B(z_2)` are the two fixed points in the argand plane and `|z-z_0|=|(baralphaz_0+alphabarz_0+r)/(2|alpha|)|`, then find locus of z?, 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|=|z_1-z_2|`, then find locus of z?, 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|=|z_1-z_2|`, then find locus of z?, 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||=|z_1-z_2|`, then find locus of z?, 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|=k`, Find locus 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|=k`, Square Root of Complex Number, Some Typical examples Based on square root of Complex number

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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)|

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_(0)|=|(bar(boldsymbol alpha)z_(0)+alphabar(z)_(0)+r)/(2| alpha|))