# SSAT Upper Level Math : How to graph complex numbers

## Example Questions

### Example Question #1 : How To Graph Complex Numbers

Multiply:

Explanation:

FOIL the product out:

### Example Question #1 : How To Graph Complex Numbers

Simplify:

Explanation:

Use the square of a binomial pattern to multiply this:

### Example Question #1 : How To Graph Complex Numbers

Multiply:

Explanation:

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

### Example Question #611 : Ssat Upper Level Quantitative (Math)

Multiply:

Explanation:

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

### Example Question #5 : How To Graph Complex Numbers

Define an operation  as follows:

For all complex numbers ,

Evaluate

Explanation:

### Example Question #6 : How To Graph Complex Numbers

Define an operation  as follows:

For all complex numbers ,

Evaluate

Explanation:

### Example Question #2 : How To Graph Complex Numbers

Evaluate .

The expression is undefined.

Explanation:

### Example Question #8 : How To Graph Complex Numbers

Define an operation  as follows:

For all complex numbers ,

Evaluate

Explanation:

Multiply both numerator and denominator by the conjugate of the denominator, , to rationalize the denominator:

### Example Question #1 : How To Graph Complex Numbers

Define an operation  as follows:

For all complex numbers ,

Evaluate .

None of the other choices gives the correct answer.

Explanation:

### Example Question #10 : How To Graph Complex Numbers

Define an operation  as follows:

For all complex numbers ,

If  and , evaluate .