### All SAT Math Resources

## Example Questions

### Example Question #1 : Complex Numbers

From , subtract its complex conjugate. What is the difference ?

**Possible Answers:**

**Correct answer:**

The complex conjugate of a complex number is , so has as its complex conjugate. Subtract the latter from the former:

### Example Question #2 : Complex Numbers

From , subtract its complex conjugate.

**Possible Answers:**

**Correct answer:**

The complex conjugate of a complex number is . Therefore, the complex conjugate of is ; subtract the latter from the former by subtracting real parts and subtracting imaginary parts, as follows:

### Example Question #3 : Complex Numbers

From , subtract its complex conjugate.

**Possible Answers:**

**Correct answer:**

The complex conjugate of a complex number is . Therefore, the complex conjugate of is ; subtract the latter from the former by subtracting real parts and subtracting imaginary parts, as follows:

### Example Question #4 : Complex Numbers

Simplify:

**Possible Answers:**

**Correct answer:**

Rewrite in their imaginary terms.

### Example Question #1 : Complex Numbers

Add and its complex conjugate.

**Possible Answers:**

**Correct answer:**

The complex conjugate of a complex number is . Therefore, the complex conjugate of is ; add them by adding real parts and adding imaginary parts, as follows:

,

the correct response.

### Example Question #6 : Complex Numbers

Add to its complex conjugate.

**Possible Answers:**

**Correct answer:**

The complex conjugate of a complex number is . Therefore, the complex conjugate of is ; add them by adding real parts and adding imaginary parts, as follows:

### Example Question #7 : Complex Numbers

An arithmetic sequence begins as follows:

Give the next term of the sequence

**Possible Answers:**

**Correct answer:**

The common difference of an arithmetic sequence can be found by subtracting the first term from the second:

Add this to the second term to obtain the desired third term:

.

### Example Question #8 : Complex Numbers

Simplify:

**Possible Answers:**

**Correct answer:**

It can be easier to line real and imaginary parts vertically to keep things organized, but in essence, combine like terms (where 'like' here means real or imaginary):

### Example Question #1 : Complex Numbers

For , what is the sum of and its complex conjugate?

**Possible Answers:**

**Correct answer:**

The complex conjugate of a complex number is , so has as its complex conjugate. The sum of the two numbers is

### Example Question #10 : Complex Numbers

Evaluate:

**Possible Answers:**

None of these

**Correct answer:**

A power of can be evaluated by dividing the exponent by 4 and noting the remainder. The power is determined according to the following table:

, so

, so

, so

, so

Substituting:

Collect real and imaginary terms:

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