All SAT Math Resources
Example Questions
Example Question #1 : Complex Numbers
Simplify:
Rewrite in their imaginary terms.
Example Question #1 : Complex Numbers
Add and its complex conjugate.
The complex conjugate of a complex number is . Therefore, the complex conjugate of is ; add them by adding real parts and adding imaginary parts, as follows:
,
the correct response.
Example Question #3 : Complex Numbers
Add to its complex conjugate.
The complex conjugate of a complex number is . Therefore, the complex conjugate of is ; add them by adding real parts and adding imaginary parts, as follows:
Example Question #2 : Complex Numbers
An arithmetic sequence begins as follows:
Give the next term of the sequence
The common difference of an arithmetic sequence can be found by subtracting the first term from the second:
Add this to the second term to obtain the desired third term:
.
Example Question #3 : Complex Numbers
Simplify:
It can be easier to line real and imaginary parts vertically to keep things organized, but in essence, combine like terms (where 'like' here means real or imaginary):
Example Question #2 : Complex Numbers
For , what is the sum of and its complex conjugate?
The complex conjugate of a complex number is , so has as its complex conjugate. The sum of the two numbers is
Example Question #3 : How To Add Complex Numbers
Evaluate:
None of these
A power of can be evaluated by dividing the exponent by 4 and noting the remainder. The power is determined according to the following table:
, so
, so
, so
, so
Substituting:
Collect real and imaginary terms:
Example Question #3 : How To Add Complex Numbers
Evaluate:
A power of can be evaluated by dividing the exponent by 4 and noting the remainder. The power is determined according to the following table:
, so
, so
, so
, so
Substituting:
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