## SAT SUBJECT TEST MATH LEVEL 2

## PART 2

## REVIEW OF MAJOR TOPICS

## CHAPTER 3

## Numbers and Operations

3.2 Complex Numbers

### GRAPHING COMPLEX NUMBERS

A complex number can be represented graphically as rectangular coordinates, with the *x* -coordinate as the real part and the *y* -coordinate as the imaginary part. The modulus of a complex number is the square of its distance to the origin. The Pythagorean theorem tells us that this distance is . The conjugate of the imaginary number *a* + *bi* is *a* – *bi* , so the graphs of conjugates are reflections about the *y* -axis. Also, the product of an imaginary number and its conjugate is the square of the modulus because (*a* + *bi* )(*a* – *bi* ) = *a *^{2} – *b *^{2}*i *^{2} = *a *^{2} + *b*^{2}.

**EXERCISES**

1. If *z* is the complex number shown in the figure, which of the following points could be *iz*?

(A) *A*

(B) *B*

(C) *C*

(D) *D*

(E) *E*

2. Which of the following is the modulus of 2 + *i?*

(A)

(B) 2

(C)

(D)

(E) 5