How do you write the following quotient in standard form #4/(4-5i)#?

1 Answer
Feb 7, 2017

Answer:

#16/41+20/41i#

Explanation:

To perform the division, we require to multiply the numerator/denominator by the #color(blue)"complex conjugate"# of the denominator. This ensures that we have a rational value on the denominator.

The conjugate of #4-5i" is "4color(red)(+)5i#

#rArr4/(4-5i)=(4(4+5i))/((4-5i)(4+5i))=(16+20i)/41#

#color(blue)"Evaluating denominator"#

#rarr[(4-5i)(4+5i)=16-20i+20i-25i^2=41]larr#

#color(orange)"Reminder "i^2=(sqrt(-1))^2=-1#

#rArr4/(4-5i)=(16+20i)/41=16/41+20/41i#