Complex Imaginary Numbers - Algebra 2
Card 0 of 248
Simplify:
Simplify:
To subtract complex numbers, subtract the real terms, then subtract the imaginary terms.
To subtract complex numbers, subtract the real terms, then subtract the imaginary terms.
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Simplify:
Simplify:
To subtract complex numbers, subtract the real terms, then subtract the imaginary terms.
To subtract complex numbers, subtract the real terms, then subtract the imaginary terms.
Compare your answer with the correct one above
Identify the real part of 
Identify the real part of
A complex number in its standard form is of the form: 
, where 
stands for the real part and 
stands for the imaginary part. The symbol 
stands for 
.
The real part in this problem is 1.
A complex number in its standard form is of the form:
The real part in this problem is 1.
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Compare your answer with the correct one above
Multiply:
Multiply:
Use the FOIL technique:
Use the FOIL technique:
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Evaluate:
Evaluate:
We can set 
in the cube of a binomial pattern:
We can set
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Evaluate 
Evaluate
To divide by a complex number, we must transform the expression by multiplying it by the complex conjugate of the denominator over itself. In the problem, 
is our denominator, so we will multiply the expression by 
to obtain:
.
We can then combine like terms and rewrite all 
terms as 
. Therefore, the expression becomes:
Our final answer is therefore 
To divide by a complex number, we must transform the expression by multiplying it by the complex conjugate of the denominator over itself. In the problem,
We can then combine like terms and rewrite all
Our final answer is therefore
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Simplify the following product:
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.
Multiply these complex numbers out in the typical way:
and recall that
which is our final answer.
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Simplify:
Simplify:
To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.
To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.
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Simplify:
Simplify:
To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.
To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.
Compare your answer with the correct one above
Simplify:
Simplify:
To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.
To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.
Compare your answer with the correct one above
Simplify:
Simplify:
To subtract complex numbers, subtract the real terms together, then subtract the imaginary terms.
To subtract complex numbers, subtract the real terms together, then subtract the imaginary terms.
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Simplify:
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 
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
Substitute in
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Simplify:
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 
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
Substitute in
Compare your answer with the correct one above
Simplify:
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 
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
Substitute in
Compare your answer with the correct one above
Simplify:
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 
.
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
Substitute in
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Simplify:
Simplify:
To get rid of the fraction, multiply the numerator and denominator by the conjugate of the denominator.
Now, multiply and simplify.
Remember that 
To get rid of the fraction, multiply the numerator and denominator by the conjugate of the denominator.
Now, multiply and simplify.
Remember that
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Simplify:
Simplify:
To get rid of the fraction, multiply the numerator and denominator by the conjugate of the denominator.
Now, multiply and simplify.
Remember that 
To get rid of the fraction, multiply the numerator and denominator by the conjugate of the denominator.
Now, multiply and simplify.
Remember that
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Write in standard form: 
Write in standard form:
Multiply by the conjugate:
Multiply by the conjugate:
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Write in standard form: 
Write in standard form:
Multiply by the conjugate:
Combine:
Simplify:
Multiply by the conjugate:
Combine:
Simplify:
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