Cracking The SAT Premium

Imaginary Numbers

An imaginary number, very simply, is the square root of a negative number. Since there is no way to have
a real number that is the square root of a negative number, mathematicians needed to come up with a way
to represent this concept when writing equations. They use an italicized lowercase “I” to do that: i =

, and the SAT will likely tell you that in any problem involving imaginary numbers.

Another common piece of information you will need to know about i is how it behaves when it is raised
to a power. Here is i raised to the powers 1 through 8. Can you complete the next four values of i in the
series?

Did you notice anything about the answer? If you said that there is a repeating pattern, then you are
correct. This pattern will be helpful in answering questions containing imaginary and complex numbers.

Complex Numbers

Complex numbers are another way in which the SAT may test the concept of imaginary numbers. A
complex number is one that has a real component and an imaginary component connected by addition or
subtraction. 8 + 7i and 3 – 4i are two examples of complex numbers.

Complex numbers might be tested in a variety of ways. You may be asked to add or subtract the complex
numbers. When you are completing these operations, you can treat i as a variable. Just combine the like
terms in these expressions and then simplify (don’t forget to distribute the subtraction sign).

Here’s an example:

2.For   i   =    ,  what    is  the result  of  subtracting (2  +   4i) from    (–5 +   6i) ?

A) –7   +   2i

B) –3   –   10i

C) 3    +   2i

D) 7    –   10i

Here’s How to Crack It

Set up the subtraction necessary.