How do you divide #(2+3i)/(4-5i)#?

1 Answer
Jan 24, 2016

Answer:

# -7/41 + 22/41 i#

Explanation:

To divide the fraction : multiply the numerator and denominator

by the 'complex conjugate' of 4 - 5i which is 4 + 5i . This

changes the denominator to a real number.

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

( distribute brackets using FOIL method )

#( 8 + 10i + 12i + 15i^2 )/(16 + 20i -20i - 25i^2) #

(Note : # i^2 = - 1 )#

# = (8 + 22i -15 )/(16 + 25 ) = (- 7 + 22i )/( 16 + 25 ) = -7/41 + 22/41 i #