# ACT Math : How to subtract complex numbers

## Example Questions

### Example Question #11 : Squaring / Square Roots / Radicals

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 #2 : How To Subtract 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 #3 : How To Subtract 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 #4 : How To Subtract 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 #5 : How To Subtract 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 ?