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SAT Math : How to subtract complex numbers

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Example Question #1 : Complex Numbers

From $\frac{3}{2} + \frac{1}{4} i$ , subtract its complex conjugate. What is the difference ?

Possible Answers:

$-\frac{1}{2} i$

$\frac{1}{2} i$

$\frac{7}{4} + \frac{7}{4} i$

Correct answer:

$\frac{1}{2} i$

Explanation:

The complex conjugate of a complex number a+bi is a - bi , so $\frac{3}{2} + \frac{1}{4} i$ has $\frac{3}{2} - \frac{1}{4} i$ as its complex conjugate. Subtract the latter from the former:

$\left (\frac{3}{2} + \frac{1}{4} i \right ) - \left ( \frac{3}{2} - \frac{1}{4} i \right )$

$= \frac{3}{2} + \frac{1}{4} i - \frac{3}{2}+ \frac{1}{4} i$

$= \frac{3}{2}- \frac{3}{2} + \frac{1}{4} i + \frac{1}{4} i$

$= \frac{1}{2} i$

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Example Question #2 : Complex Numbers

From $17 - i \sqrt{17}$ , subtract its complex conjugate.

Possible Answers:

$2 i \sqrt{17}$

$- 2 i \sqrt{17}$

Correct answer:

$- 2 i \sqrt{17}$

Explanation:

The complex conjugate of a complex number a - bi is a+ bi . Therefore, the complex conjugate of $17 - i \sqrt{17}$ is $17 + i \sqrt{17}$ ; subtract the latter from the former by subtracting real parts and subtracting imaginary parts, as follows:

$(17 - i \sqrt{17})- (17 + i \sqrt{17})$

$= 17 - i \sqrt{17} - 17 - i \sqrt{17}$

$= 17 - 17 - i \sqrt{17} - i \sqrt{17}$

$= - 2 i \sqrt{17}$

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Example Question #3 : Complex Numbers

From $7 + i \sqrt {7 }$ , subtract its complex conjugate.

Possible Answers:

$-2i \sqrt {7 }$

$2i \sqrt {7 }$

Correct answer:

$2i \sqrt {7 }$

Explanation:

The complex conjugate of a complex number a+ bi is a - bi . Therefore, the complex conjugate of $7 + i \sqrt {7 }$ is $7 - i \sqrt {7 }$ ; subtract the latter from the former by subtracting real parts and subtracting imaginary parts, as follows:

$(7 + i \sqrt {7 })- (7 - i \sqrt {7 })$

$= 7- 7 + i \sqrt {7 }- (- i \sqrt {7 })$

$= i \sqrt {7 }+ i \sqrt {7 }$

$=2i \sqrt {7 }$

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SAT Math : How to subtract complex numbers

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Complex Numbers

Example Question #2 : Complex Numbers

Example Question #3 : Complex Numbers

All SAT Math Resources

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