All GRE Subject Test: Math Resources
Example Questions
Example Question #1 : Irrational Numbers
Evaluate:
We can set in the cube of a binomial pattern:
Example Question #1 : Imaginary Numbers
Simplify the following product:
Multiply these complex numbers out in the typical way:
and recall that by definition. Then, grouping like terms we get
which is our final answer.
Example Question #2 : Irrational Numbers
Simplify:
Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.
Remember that , so
.
Substitute in for
Example Question #11 : Number Theory
Simplify:
Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.
Remember that , so
.
Substitute in for
Example Question #12 : Number Theory
Simplify:
Start by using FOIL. Which means to multiply the first terms together then the outer terms followed by the inner terms and lastly, the last terms.
Remember that , so
.
Substitute in for
Example Question #1 : Equations With Complex Numbers
Solve for and
:
Remember that
So the powers of are cyclic. This means that when we try to figure out the value of an exponent of
, we can ignore all the powers that are multiples of
because they end up multiplying the end result by
, and therefore do nothing.
This means that
Now, remembering the relationships of the exponents of , we can simplify this to:
Because the elements on the left and right have to correspond (no mixing and matching!), we get the relationships:
No matter how you solve it, you get the values ,
.
Example Question #61 : Algebra
Simplify:
None of the Above
Step 1: Split the into
.
Step 2: Recall that , so let's replace it.
We now have: .
Step 3: Simplify . To do this, we look at the number on the inside.
.
Step 4: Take the factorization of and take out any pairs of numbers. For any pair of numbers that we find, we only take
of the numbers out.
We have a pair of , so a
is outside the radical.
We have another pair of , so one more three is put outside the radical.
We need to multiply everything that we bring outside:
Step 5: The goes with the 9...
Step 6: The last after taking out pairs gets put back into a square root and is written right after the
It will look something like this:
Example Question #1 : Imaginary Numbers & Complex Functions
There are two ways to simplify this problem:
Method 1:
Method 2:
Example Question #251 : Gre Subject Test: Math
Example Question #1 : Imaginary Roots Of Negative Numbers
All GRE Subject Test: Math Resources
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