ACT Math : Complex Numbers
Study concepts, example questions & explanations for ACT Math
All ACT Math Resources
Example Questions
Example Question #1 : Complex Numbers
Subtract 
A complex number is a combination of a real and imaginary number. To subtract complex numbers, subtract each element separately.
In equation 
Example Question #1 : Complex Numbers
Simplify the exponent,
When you have an exponent on the outside of parentheses while another is on the inside of the parentheses, such as in 
This is different than when you have two numbers with the same base multiplied together, such as in 
Example Question #3 : Complex Numbers
Complex numbers take the form 
Simplify:
Solving this equation is very similar to solving a linear binomial like 
Example Question #4 : Complex Numbers
Complex numbers take the form 
Which of the following is incorrect?
A problem like this can be solved similarly to a linear binomial like 
Example Question #5 : Complex Numbers
Complex numbers take the form 
Which of the following equations simplifies into 
This equation can be solved very similarly to a binomial like 
Example Question #6 : Complex Numbers
Suppose 
Evaluate the following expression:
Substituting for 
This simplifies to
which equals
Example Question #1 : Complex Numbers
What is the solution of the following equation?
A complex number is a combination of a real and imaginary number. To add complex numbers, add each element separately.
First, distribute:
Then, group the real and imaginary components:
Solve to get:
Example Question #8 : Complex Numbers
What is the sum of 
and
A complex number is a combination of a real and imaginary number. To add complex numbers, add each element separately.
In equation 
In equation 
When added,
Example Question #9 : Complex Numbers
Complex numbers take the form 
Simplify:
When adding or subtracting complex numbers, the real terms are additive/subtractive, and so are the nonreal terms.
Example Question #10 : Complex Numbers
Complex numbers take the form 
Can you add the following two numbers: 
Complex numbers take the form a + bi, where a is the real term in the complex number and bi is the nonreal (imaginary) term in the complex number. Taking this, we can see that for the real number 8, we can rewrite the number as 
Thus, any real number can be added to any complex number simply by considering the nonreal portion of the number to be 
All ACT Math Resources
