Precalculus : Products and Quotients of Complex Numbers in Polar Form

Study concepts, example questions & explanations for Precalculus

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Example Questions

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Example Question #13 : Find The Quotient Of Complex Numbers

Divide.

Possible Answers:

Correct answer:

Explanation:

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator.

To find the conjugate, just change the sign in the denominator. The conjugate used will be .

Now, distribute and simplify.

Recall that 

Example Question #21 : Products And Quotients Of Complex Numbers In Polar Form

Divide

Possible Answers:

Correct answer:

Explanation:

Start by simplifying the fraction.

Recall that 

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator.

To find the conjugate, just change the sign in the denominator. The conjugate used will be .

Now, distribute and simplify.

Recall that 

Example Question #15 : Find The Quotient Of Complex Numbers

Simplify  into a number of the form .

Possible Answers:

None of the other answers.

Correct answer:

Explanation:

We have

 

Multiply by the complex conjugate of the denominator.

The complex conjugate is the denominator with the sign changed:

 

Multiply fractions

 

 FOIL the numerator and denominator

 

Apply the rule of :

   

 Simplify.

 

Simplify further using the addition of fractions rule, then factor the i out of the 2nd fraction.

 

Example Question #16 : Find The Quotient Of Complex Numbers

Divide:

Possible Answers:

Correct answer:

Explanation:

To divide complex numbers, multiply both the numerator and denominator by the conjugate of the denominator.

To find the conjugate, just change the sign in the denominator. The conjugate used will be .

Now, distribute and simplify.

Recall that 

Then combine like terms:

Then since each term is a multiple of  you can simplify:

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