How do you divide (4+5i)/(2-3i)?
2 Answers
Multiply both numerator and denominator by the Complex conjugate of the denominator, then simplify to find:
(4+5i)/(2-3i)=-7/13 + 22/13i
Explanation:
Multiply numerator and denominator by
(4+5i)/(2-3i)
=((4+5i)(2+3i))/((2-3i)(2+3i))
=(stackrel "First" overbrace((4*2))+stackrel "Outside" overbrace((4*3i))+stackrel "Inside" overbrace((5i*2))+stackrel "Last" overbrace((5i*3i)))/(2^2+3^2)
=(8+12i+10i-15)/(4+9)
=(-7+22i)/13
=-7/13 + 22/13i
Explanation:
Whenever we divide complex numbers we multiply both numerator and denominator with the complex conjugate of the denominator, this makes the denominator a real number
If the complex number is
For example
Now back to our problem.