SAT SUBJECT TEST MATH LEVEL 1
Imaginary and 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.