### All ACT Math Resources

## Example Questions

### Example Question #1 : Complex Numbers

Subtract from , given:

**Possible Answers:**

**Correct answer:**

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,

.

**Possible Answers:**

**Correct answer:**

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 #21 : Squaring / Square Roots / Radicals

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:

**Possible Answers:**

**Correct answer:**

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?

**Possible Answers:**

**Correct answer:**

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 ?

**Possible Answers:**

**Correct answer:**

This equation can be solved very similarly to a binomial like .

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