GRE Subject Test: Math : Operations on Complex Numbers

Study concepts, example questions & explanations for GRE Subject Test: Math

varsity tutors app store varsity tutors android store

Example Questions

← Previous 1 3

Example Question #1 : Operations On Complex Numbers

Expand and Simplify: 

Possible Answers:

Correct answer:

Explanation:

Step 1: We will multiply the two complex conjugates:  and .



Step 2: Replace  with .



Simplify:





Step 3: Multiply the result of the complex conjugates to the other parentheses,.



The final answer after the product of all three binomials is 
 

Example Question #1 : Operations On Complex Numbers

Expand: .

Possible Answers:

Correct answer:

Explanation:

Quick Way:
Step 1: Expand  .

.

Remember: 



Step 2: 

By this equivalence, I can just raise the answer of  to the power .



. Replace ..

Final answer: 

Long Way:



Math work

Example Question #1 : Operations On Complex Numbers

Multiply: 

Possible Answers:

Correct answer:

Explanation:

Step 1: FOIL:

Recall, FOIL means to multiply the first terms in both binomials together, the outer terms together, the inner terms together, and finally, the last terms together.



Step 2: Simplify:



Step 3: Recall: . Replace and simplify.



Example Question #3 : Operations On Complex Numbers

Possible Answers:

Correct answer:

Explanation:

When adding imaginary numbers, simply add the real parts and the imaginary parts. 

Example Question #81 : Algebra

 

Possible Answers:

Correct answer:

Explanation:

Example Question #82 : Algebra

What is the value of ?

Possible Answers:

None of the other answers

Correct answer:

Explanation:

Distribute and Multiply:

Simplify all terms...

Example Question #83 : Algebra

What is the value: ?

Possible Answers:

Correct answer:

Explanation:

Step 1: Recall the cycle of imaginary numbers to a random power .

If , then 

If , then 

If , then 

If , then 

If , then 

and so on....

The cycle repeats every  terms. 

For ANY number , you can break down that term into smaller elementary powers of i. 

Step 2: Distribute the  to all terms in the parentheses:

.

Step 3: Recall the rules for exponents:

Step 4: Use the rules to rewrite the expression in Step 2:

Step 5: Simplify the results in Step 4. Use the rules in Step 1.:

Step 6: Write the answer in  form, where  is the real part and  is the imaginary part:

We get 

Example Question #84 : Algebra

Possible Answers:

Correct answer:

Explanation:

When adding complex numbers, we add the real numbers and add the imaginary numbers. 

 

 

Example Question #21 : Imaginary Numbers & Complex Functions

Possible Answers:

Correct answer:

Explanation:

In order to subtract complex numbers, we must first distribute the negative sign to the second complex number. 

 

Example Question #22 : Imaginary Numbers & Complex Functions

Possible Answers:

Correct answer:

Explanation:

First we must distribute

 

 

 

← Previous 1 3
Learning Tools by Varsity Tutors