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Example Questions
Example Question #131 : Review And Other Topics
Simplify:
When simplifying expressions with complex numbers, use the same techniques and procedures as normal.
Distribute the sign to the terms in parentheses:
Combine like terms- combine the real numbers together and the imaginary numbers together:
This gives a final answer of -1+9i
Example Question #132 : Review And Other Topics
Simplify:
When simplifying expressions with complex numbers, use the same techniques and procedures as normal.
Distribute the sign to the terms in parentheses:
Combine like terms- combine the real numbers together and the imaginary numbers together:
This gives a final answer of 10-4i
Example Question #21 : Complex Numbers
Simplify:
When simplifying expressions with complex numbers, use the same techniques and procedures as normal.
Distribute the sign to the terms in parentheses:
Combine like terms- combine the real numbers together and the imaginary numbers together:
This gives a final answer of -8+9i
Example Question #132 : Review And Other Topics
Simplify:
When simplifying expressions with complex numbers, use the same techniques and procedures as normal.
Distribute the sign to the terms in parentheses:
Combine like terms- combine the real numbers together and the imaginary numbers together:
This gives a final answer of 9-5i
Example Question #23 : Complex Numbers
Simplify:
When simplifying expressions with complex numbers, use the same techniques and procedures as normal.
Distribute the sign to the terms in parentheses:
Combine like terms- combine the real numbers together and the imaginary numbers together:
This gives a final answer of 9+9i
Example Question #24 : Complex Numbers
Simplify:
When simplifying expressions with complex numbers, use the same techniques and procedures as normal.
Distribute the sign to the terms in parentheses:
Combine like terms- combine the real numbers together and the imaginary numbers together:
This gives a final answer of 18-i
Example Question #25 : Complex Numbers
Simplify:
When simplifying expressions with complex numbers, use the same techniques and procedures as normal.
Distribute the sign to the terms in parentheses:
Combine like terms- combine the real numbers together and the imaginary numbers together:
This gives a final answer of 4-i
Example Question #21 : Complex Numbers
Rewrite in standard form:
None of these
Multiply ply by the conjugate:
Simplify:
Example Question #134 : Review And Other Topics
Rewrite in standard form:
None of these
Find a common denominator and subtract.
To do so multiply the numerator and denominator of both fractions by the denominator of the opposite fraction:
Combine and simplify:
Keep in mind
Example Question #2 : How To Find A Solution Set
Give all real solutions of the following equation:
By substituting - and, subsequently,
this can be rewritten as a quadratic equation, and solved as such:
We are looking to factor the quadratic expression as , replacing the two question marks with integers with product
and sum 5; these integers are
.
Substitute back:
The first factor cannot be factored further. The second factor, however, can itself be factored as the difference of squares:
Set each factor to zero and solve:
Since no real number squared is equal to a negative number, no real solution presents itself here.
The solution set is .
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