Precalculus : Polar Coordinates and Complex Numbers

Study concepts, example questions & explanations for Precalculus

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Example Questions

Example Question #1 : Find The Quotient Of Complex Numbers

Write 

 

in the form  for some real numbers  and 

Possible Answers:

Correct answer:

Explanation:

The correct answer is 

Using simple algebra and multiplying the expression by the complex conjugate of the denominator, we get:

Example Question #4 : 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 #5 : 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 #6 : 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 #7 : 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 #8 : 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 #9 : 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 #10 : 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 #11 : 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 #12 : 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 

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