Question

Let α and β be the roots of the equation x 2 + (2 i – 1) = 0. Then, the value of |α2 + β2| is equal to

• A. 50
• B. 250
• C. 1250
• D. 1500

Answer 1

Answer: (A)

50

Answer 2

The correct option is(A): 50

x 2 + 2 i – 1 = 0

α2 = β2 = 1 – 2 i

α4 = (1 – 2 i)2 = 1 + (2 i)2 – 4 i = –3 – 4 i

α8 = (–3 – 4 i)2 = 9 – 16 + 24 i = –7 + 24 i

$=\sqrt{(-7)^2+(24)^2}=50$