Let denote the real part of the complex number z = 5 + 2i 2 - 5i + 20 + 5i 7 + 6i + 3i

MATHEMATICS · Subjective · CBSE · Mathematics · Complex Numbers and Quadratic Equations · Complex Numbers and Quadratic Equations

Problem

Let

S

denote the real part of the complex number

z = \frac{5 + 2i}{2 - 5i} + \frac{20 + 5i}{7 + 6i} + 3i,

where

i = \sqrt{-1}

. Let

K

denote the sum of the imaginary parts of the roots of the equation

z^2 - 8(1 - i)z + 63 - 16i = 0

, and let

G

denote the value of

\sum_{r=4}^{2012} i^r,

where

i = \sqrt{-1}

. Find the value of

S - K + G