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Complex Numbers and Quadratic Equations

If arg (z – 1) = arg (z + 3i), then find x – 1 : y. where z = x + iy

CBSE, Complex Numbers and Quadratic Equations, Maths, NCERT Exemplar

Let \[z\text{ }=\text{ }x\text{ }+\text{ }iy\] Given that, \[arg\text{ }\left( z-\text{ }\text{ }1 \right)\text{ }=\text{ }arg\text{ }\left( z\text{ }+\text{ }3i \right)\] \[\Rightarrow ~arg\text{...

If the real part of ( z̅ + 2)/ ( z̅ – 1) is 4, then show that the locus of the point representing z in the complex plane is a circle.

CBSE, Class 11, Complex Numbers and Quadratic Equations, Maths, NCERT Exemplar

Let z = x + iy Now, \[\Rightarrow ~{{x}^{2}}~+\text{ }x\text{ }\text{ }-2\text{ }+\text{ }{{y}^{2}}~=\text{ }4\text{ }\left( {{x}^{2}}~\text{ }-2x\text{ }+\text{ }1\text{ }+\text{ }{{y}^{2}}...

If arg (z – 1) = arg (z + 3i), then find x – 1 : y. where z = x + iy

If the real part of ( z̅ + 2)/ ( z̅ – 1) is 4, then show that the locus of the point representing z in the complex plane is a circle.

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