## Example Questions

### Example Question #1 : How To Subtract Complex Numbers

Subtract from , given:        Explanation:

A complex number is a combination of a real and imaginary number. To subtract complex numbers, subtract each element separately.

In equation  is the real component and is the imaginary component (designated by ). In equation  is the real component and is the imaginary component. Solving for , ### Example Question #1 : Complex Numbers

Simplify the exponent, .     Explanation:

When you have an exponent on the outside of parentheses while another is on the inside of the parentheses, such as in , multiply the exponents together to get the answer: .

This is different than when you have two numbers with the same base multiplied together, such as in . In that case, you add the exponents together.

### Example Question #1 : Complex Numbers

Complex numbers take the form , where is the real term in the complex number and is the nonreal (imaginary) term in the complex number.

Simplify:       Explanation:

Solving this equation is very similar to solving a linear binomial like . To solve, just combine like terms, being careful to watch for double negatives.    ### Example Question #1 : Complex Numbers

Complex numbers take the form , where is the real term in the complex number and is the nonreal (imaginary) term in the complex number.

Which of the following is incorrect?      Explanation:

A problem like this can be solved similarly to a linear binomial like /   ### Example Question #1 : Complex Numbers

Complex numbers take the form , where is the real term in the complex number and is the nonreal (imaginary) term in the complex number.

Which of the following equations simplifies into ?      Explanation:

This equation can be solved very similarly to a binomial like .   ### All ACT Math Resources 