All SAT Math Resources
Example Questions
Example Question #24 : Complex Numbers
Raise to the power of 3.
None of the other choices gives the correct response.
To raise any expression to the third power, use the pattern
Setting :
Taking advantage of the Power of a Product Rule:
Since ,
and
:
Collecting real and imaginary terms:
Example Question #31 : Complex Numbers
Evaluate .
None of the other choices gives the correct response.
Apply the Power of a Product Rule:
,
and
,
so, substituting and evaluating:
Example Question #32 : Complex Numbers
Raise to the power of 4.
The easiest way to find is to note that
.
Therefore, we can find the fourth power of by squaring , then squaring the result.
Using the binomial square pattern to square :
Applying the Power of a Product Property:
Since by definition:
Square this using the same steps:
,
the correct response.
Example Question #31 : Complex Numbers
Evaluate
None of the other choices gives the correct response.
None of the other choices gives the correct response.
Apply the Power of a Product Rule:
Applying the Product of Powers Rule:
raised to any multiple of 4 is equal to 1, and , so, substituting and evaluating:
This is not among the given choices.
Example Question #44 : Squaring / Square Roots / Radicals
; is the complex conjugate of .
Evaluate
.
conforms to the perfect square trinomial pattern
.
The easiest way to solve this problem is to add and , then square the sum.
The complex conjugate of a complex number is .
,
so is the complex conjugate of this;
,
and
Substitute 14 for :
.
Example Question #45 : Squaring / Square Roots / Radicals
; is the complex conjugate of .
Evaluate
.
conforms to the perfect square trinomial pattern
.
The easiest way to solve this problem is to add and , then square the sum.
The complex conjugate of a complex number is .
,
so is the complex conjugate of this;
,
and
Substitute 8 for :
.
Example Question #46 : Squaring / Square Roots / Radicals
; is the complex conjugate of .
Evaluate
.
conforms to the perfect square trinomial pattern
.
The easiest way to solve this problem is to subtract and , then square the difference.
The complex conjugate of a complex number is .
,
so is the complex conjugate of this;
Substitute for :
By definition, , so, substituting,
,
the correct choice.
Example Question #2401 : Sat Mathematics
Remember that .
Simplify:
Use FOIL to multiply complex numbers as follows:
Since , it follows that , so then:
Combining like terms gives:
Example Question #11 : How To Multiply Complex Numbers
Simplify:
Use FOIL:
Combine like terms:
But since , we know
Example Question #49 : Squaring / Square Roots / Radicals
; is the complex conjugate of .
Evaluate
.
conforms to the perfect square trinomial pattern
.
The easiest way to solve this problem is to subtract and , then square the difference.
The complex conjugate of a complex number is .
,
so is the complex conjugate of this;
Taking advantage of the Power of a Product Rule and the fact that :