a 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.
b 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.
