To find the location on a coordinate plane we first look at the -axis, which runs horizontal and then the -axis, which runs vertical. We write the point on the -axis first, followed by the point on the -axis.

The orange triangle is over on the -axis and up on the -axis.

To find the location on a coordinate plane we first look at the -axis, which runs horizontal and then the -axis, which runs vertical. We write the point on the -axis first, followed by the point on the -axis.

The orange triangle is over on the -axis and up on the -axis.

The complex conjugate of a complex number is , so the complex conjugate of is . Multiply this by :

This is a product of an imaginary number and its complex conjugate, so it can be evaluated using this formula:

The complex conjugate of a complex number is . Since , its complex conjugate is itself. Multiply this by :

The complex conjugate of a complex number is . Since , its complex conjugate is .

Multiply this by :

Recall that by definition .

The starting point is at . When we move up or down we are moving along the -axis. When we move to the right or left we are moving along the -axis.

Moving up the -axis and moving right on the -axis means addition.

Moving down the -axis and moving left on the axis means subtraction.

Because we are moving up , we can add to our coordinate point and because we are moving to the left we can subtract from our coordinate point.

FOIL the product out:

To FOIL multiply the first terms from each binomial together, multiply the outer terms of both terms together, multiply the inner terms from both binomials together, and finally multiply the last terms from each binomial together.

Recall that i is an imaginary number and by definition . Substituting this into the function is as follows.

The complex conjugate of a complex number is , so has as its complex conjugate; the sum of the two numbers is

The product of a complex number and its conjugate is

which will always be a real number. Therefore, all four given choices, all of which are imaginary, can be immediately eliminated. The correct response is that the correct answer is not given among the other responses.