SAT Math : Complex Numbers

Example Questions

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Example Question #1 : Complex Numbers

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

Explanation:

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.

Explanation:

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.

Explanation:

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:

Explanation:

Rewrite  in their imaginary terms.

Example Question #1 : How To Add Complex Numbers

Explanation:

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

Explanation:

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

Explanation:

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:

Explanation:

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 #21 : New Sat Math No Calculator

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

Explanation:

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:

None of these

Explanation:

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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