### All ACT Math Resources

## Example Questions

### Example Question #1 : Complex Numbers

Suppose and

Evaluate the following expression:

**Possible Answers:**

**Correct answer:**

Substituting for and , we have

This simplifies to

which equals

### Example Question #7 : Complex Numbers

What is the solution of the following equation?

**Possible Answers:**

**Correct answer:**

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 given

and

?

**Possible Answers:**

**Correct answer:**

A complex number is a combination of a real and imaginary number. To add complex numbers, add 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.

When added,

### Example Question #9 : Complex Numbers

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

Simplify:

**Possible Answers:**

**Correct answer:**

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 , where *a* is the real term in the complex number and *bi* is the nonreal (imaginary) term in the complex number.

Can you add the following two numbers: ? If so, what is their sum?

**Possible Answers:**

**Correct answer:**

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 , where represents the (zero-sum) non-real portion of the complex number.

Thus, any real number can be added to any complex number simply by considering the nonreal portion of the number to be .

### 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.

Which of the following is incorrect?

**Possible Answers:**

**Correct answer:**

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

Thus, to balance the equation, add like terms on the left side.

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