﻿ GRAPHING COMPLEX NUMBERS - Complex Numbers - Numbers and Operations - REVIEW OF MAJOR TOPICS - SAT SUBJECT TEST MATH LEVEL 2 ﻿

## PART 2 ## REVIEW OF MAJOR TOPICS ## 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

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