Let z be a complex number such that z - i z + 2 i = 1 and z = 5 2 . Then the value of z + 3 i is

Question

Let z be a complex number such that z - i z + 2 i = 1 and z = 5 2 . Then the value of z + 3 i is, 10, 7 2, 15 4, 2 3

MARKS App · Accepted Answer

Given, z - i = z + 2 i ⇒ x 2 + y - 1 2 = x 2 + y + 2 2 ⇒ - 2 y + 1 = 4 y + 4 ⇒ 6 y = - 3 ⇒ y = - 1 2 From, z = 5 2 , we get, x 2 + y 2 = 25 4 ⇒ x 2 = 24 4 = 6 ⇒ z = ± 6 - i 2 Hence, z + 3 i = 6 + 25 4 = 49 4 z + 3 i = 7 2

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