To write a quotient as a single complex number, multiply the numerator and the denominator by the complex conjugate of the denominator.
B
b
The complex conjugate of the denominator is 1-2i.
A
a
-1/5-7/5i
B
b
1-2i
Practice makes perfect
a
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 now.
Denominator:& 4+2i
Complex Conjugate:& 4-2iThe 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.
2-6i/4+2i*4-2i/4-2i
This process is also known as rationalizing the denominator. Doing so will simplify the quotient.
Similarly as in Part A, write the complex conjugate of the denominator of the given expression.
Denominator:& 1+2i
Complex Conjugate:& 1-2iThe 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.
5/1+2i*1-2i/1-2i
This process is also known as rationalizing the denominator. Doing so will simplify the quotient.
