Reduce (1/(1 - 4i) - 2/(1 + i) ((3-4i) / (5+i)) to the standard form

Solution:

(1/(1 - 4i) - 2/(1 + i) ((3-4i) / (5+i))

= [ (1+i) - 2(1-4i)]/((1-4i)(1+i)) · ((3-4i) / (5+i))

= (1+i-2+8i) / (1+i-4i+4i²) ·  ((3-4i) / (5+i))

= (-1+9i) / (-5-3i) · ((3-4i) / (5+i))

= (-3 + 4i + 27i - 36i²) / (25 + 5i -15i - 3i²)

= (33 + 31i) / (28 - 10i)

= (33 + 31i) / (28 - 10i) · (28 + 10i) / (28 + 10i) (Rationalizing the denominator)

= (614 + 1198i) / (884)

= 307/442 + 599i/442

NCERT Solutions Class 11 Maths Chapter 5 Exercise ME Question 3

Reduce (1/(1 - 4i) - 2/(1 + i) ((3-4i) / (5+i)) to the standard form

Summary:

( 1/(1 - 4i) - 2/(1 + i) ((3-4i) / (5+i)) in standard form becomes 307/442 + 599i / 422