All GRE Subject Test: Math Resources
Example Questions
Example Question #1 : Operations On Complex Numbers
Expand and Simplify:
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: .
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:
Example Question #1 : Operations On Complex Numbers
Multiply:
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 #1 : Operations On Complex Numbers
When adding imaginary numbers, simply add the real parts and the imaginary parts.
Example Question #2 : Operations On Complex Numbers
Example Question #4 : Operations On Complex Numbers
What is the value of ?
None of the other answers
Distribute and Multiply:
Simplify all terms...
Example Question #5 : Operations On Complex Numbers
What is the value: ?
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 #1 : Operations On Complex Numbers
When adding complex numbers, we add the real numbers and add the imaginary numbers.
Example Question #2 : Operations On Complex Numbers
In order to subtract complex numbers, we must first distribute the negative sign to the second complex number.
Example Question #1 : Operations On Complex Numbers
First we must distribute
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