To write a quotient as a complex number, multiply the numerator and the denominator by the complex conjugate of the denominator.
3/5+7/15i
Practice makes perfect
Recall that the number pairs a+bi and a-bi are complex conjugates. To write the complex conjugate of a complex number, we only change the sign of the imaginary part. Let's do that for the denominator of our given expression.
Denominator:& 6-3i
Complex Conjugate:& 6+3iThe product of complex conjugates is a real number. To write the given quotient as a complex number, we will multiply the numerator and the denominator by the complex conjugate of the denominator.
5+i/6-3i*6+3i/6+3i
This process is also known as rationalizing the denominator. Doing so will simplify the quotient.
