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

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Correct option is D

Given |z-i|2=|z+2i|2 ⇒x2+(y-1)2=x2+(y+2)2⇒-2y+1=4y+4⇒y=-12 Given |z|=52 It gives x2+y2=254x2=244=6x=±6 It gives z=±6-i2 The required value is |z+3i|=6+5i2=6+254=∣72

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Let z be a complex number such that z-iz+2i=1 and |z|=52, Then the value of z+3i is:

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