SAT SUBJECT TEST MATH LEVEL 1

MISCELLANEOUS TOPICS

CHAPTER 17
Imaginary and Complex Numbers

COMPLEX NUMBERS

The imaginary unit can be added to and multiplied by real numbers to form complex numbers. Every complex number can be written in the form a + bi, where a and b are real numbers. a is called the real part and bi the imaginary part of the complex number a + bi. Two complex numbers are equal if, and only if, their real parts are equal and their imaginary parts are equal.

Key Fact P3

If a + bi = c + di, then a = c and b = d.

EXAMPLE 4: If 2(3 + yi ) = x + 8i, what are the values of x and y ?

x + 8i = 2(3 + yi ) x + 8i = 6 + 2yi
So, x = 6 and 8 = 2y ⇒ x = 6 and y = 4

The arithmetic of complex numbers follows all the rules you are familiar with for real numbers.

Key Fact P4

• To add complex numbers, add their real parts and add their imaginary parts. For example:

(3 + 5i ) + (2 + 3i ) = 5 + 8i

• To subtract complex numbers, subtract their real parts and subtract their imaginary parts. For example:

(3 + 5i ) – (2 + 3i ) = 1 + 2i

• To multiply complex numbers, “FOIL” them as if they were binomials and replace i 2 by –1. For example:

Complex numbers can also be divided, but you do not need to know how to do this for the Math 1 test.