Complex Imaginary Numbers - Algebra 2

To subtract complex numbers, subtract the real terms, then subtract the imaginary terms.

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.

Use the FOIL technique:

We can set in the cube of a binomial pattern:

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

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.

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.

To add complex numbers, find the sum of the real terms, then find the sum of the imaginary terms.

To subtract complex numbers, subtract the real terms together, then subtract the imaginary terms.

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 , 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 , 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 , so .

Substitute in for .

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

Multiply by the conjugate:

Multiply by the conjugate:

Combine:

Simplify: