Understanding Imaginary and Complex Numbers - Math

Combine like terms. Treat as if it were any other variable.

Substitute to eliminate .

Simplify.

First, factor the term in the radical.

Now, we can simplify.

FOIL:

Since and are conmplex conjugates, they can be multiplied according to the following pattern:

Since and are conmplex conjugates, they can be multiplied according to the following pattern:

can be evaluated by dividing by 4 and noting the remainder. Since - that is, since dividing 45 by 4 yields remainder 1:

Recall the basic property of imaginary numbers, .

Keeping this in mind, .

Recall that .

Then, we have that .

Note that we used the power rule of exponents and the order of operations to simplify the exponent before multiplying by the coefficient.

The absolute value is a measure of the distance of a point from the origin. Using the pythagorean distance formula to calculate this distance.

Combine like terms. Treat as if it were any other variable.

Substitute to eliminate .

Simplify.

First, factor the term in the radical.

Now, we can simplify.

FOIL:

Since and are conmplex conjugates, they can be multiplied according to the following pattern:

Since and are conmplex conjugates, they can be multiplied according to the following pattern:

can be evaluated by dividing by 4 and noting the remainder. Since - that is, since dividing 45 by 4 yields remainder 1:

Recall the basic property of imaginary numbers, .

Keeping this in mind, .

Recall that .

Then, we have that .

Note that we used the power rule of exponents and the order of operations to simplify the exponent before multiplying by the coefficient.