(A) Let $z = x + iy$. The equation is $2|x + i(y + 3)| = |x + i(y - 1)|$.Squaring both sides,we get $4(x^2 + (y + 3)^2) = x^2 + (y - 1)^2$.$4x^2 + 4(y

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a circle with radius $\frac{8}{3}$

(A) Let $z = x + iy$. The equation is $2|x + i(y + 3)| = |x + i(y - 1)|$.Squaring both sides,we get $4(x^2 + (y + 3)^2) = x^2 + (y - 1)^2$.$4x^2 + 4(y^2 + 6y + 9) = x^2 + y^2 - 2y + 1$.$3x^2 + 3y^2 + 26y + 35 = 0$.Dividing by $3$,we get $x^2 + y^2 + \frac{26}{3}y + \frac{35}{3} = 0$.This is the equation of a circle $x^2 + y^2 + 2gy + c = 0$ where $g = \frac{13}{3}$.The radius $r = \sqrt{g^2 - c} = \sqrt{(\frac{13}{3})^2 - \frac{35}{3}} = \sqrt{\frac{169}{9} - \frac{105}{9}} = \sqrt{\frac{64}{9}} = \frac{8}{3}$.

Class 11 Mathematics 1 Complex Numbers and Quadratic Equations: Complex Numbers Geometry of complex numbers

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Let $z \in \mathbb{C}$ be a complex number. The equation $2|z + 3i| - |z - i| = 0$ represents:

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a circle with radius $\frac{8}{3}$
B
a circle with diameter $\frac{10}{3}$
C
an ellipse with length of major axis $\frac{16}{3}$
D
an ellipse with length of minor axis $\frac{16}{9}$

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Let $z \in \mathbb{C}$ be a complex number. The equation $2|z + 3i| - |z - i| = 0$ represents:

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