Let z be a complex number such that Then the value of |z + 3i| is :

Engineering

Mathematics

Conjugate Modulus and Argument of a Complex Number

Question

Let z be a complex number such that $| \frac{z - i}{z + 2 i} | = 1 and | z | = \frac{5}{2} .$ Then the value of |z + 3i| is :

$\frac{7}{2}$

$\sqrt{10}$

$\frac{15}{4}$

$2 \sqrt{3}$

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x² + (y–1)² = x² + (y+2)²

– 2y + 1 = 4y + 4

6y = – 3 ⇒ y = – 1/2

$x^{2} + y^{2} = \frac{25}{4} \Rightarrow x^{2} = \frac{24}{4} = 6 \Rightarrow z = \pm \sqrt{6} - \frac{i}{2}$

$| z + 3 i | = \sqrt{6 + \frac{25}{4}} = \sqrt{\frac{49}{4}}$

$| z + 3 i | = \frac{7}{2}$