Question

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

Class X1 - Maths -Complex Numbers and Quadratic Equations Page 112

Answer 1

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

= {(1+i-2(1-4i)}/(1-4i)(1+i) × (3-4i)/(5+i)
= (9i -1)(3-4i)/(1-4i)(1+i)(5+i)
= (-3 +4i +27i -36i²)/{1(1+I)-4i(1+i)}(5+i)
= {-3 + 31i -36(-1)}/(1+i-4i-4i²)(5+i)
= {33 +31i}/(1-3i+4)(5+i)
= (33+31i)/(5-3i)(5+i)
= (33+ 31i)/(25 +5i -15i -3i²)
= (33 + 31i)/(25 -10i +3)
= (33+31i)(28 +10i)/(28-10i)(28+10i)
= {33(28+10i)+31i(28+10i)}/(28²+10²)
= {924 + 330i + 868i +310i²}/884
= {614 + 1198i}/884
= (307 + 599i)/442

Hence, (307/442) + (599/442)i

Answer 2

Answer is in the attachment...

Hope this helps