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 ) = 2 – 22 = 2 + b2.

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