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Question:

If a > 0 and z = (1 + i)^2a - i, has magnitude √(25), then z̅ is equal to:

-15 + 35i

-35 - 15i

-15 - 35i

15 - 35i

Solution:

Correct option is C. -15 - 35i
Given a > 0
z = (1 + i)^2a - i = 2a(a + i) / (a^2 + 1)
Also |z| = 25 ⇒ 2a^2 + 1 = 25 ⇒ a = 3
So z̅ = -2ai(3 - i) / 10 = -15 - 35i/5