Question

Express (3-2i)(2+3i)/(1+2i)(2-i) in the form a+ib

Answer 1

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

6+9i-4i-6i^2/2-i+4i-2i^2

6+5i-6(-1) / 2+3i-2(-1).. (because i^=-1)

6+5i+6 / 2+3i+2

12+5i / 4+3i

(12+5i)(4-3i)/(4+3i)(4-3i) (taking

conjugate)

48-36i+20i-15i^2/ (4)^2-(3i)^2

48-16i-15(-1) / 16 -9(-1)..(because i^2

= (-1) )

48-16i+5 / 16+9

53-16i / 25

hence, a+bi= 53-16i/25