ACT Math : How to subtract complex numbers

Study concepts, example questions & explanations for ACT Math

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Example Questions

Example Question #1 : Complex Numbers

Subtract  from , given:

Possible Answers:

Correct answer:

Explanation:

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 #14 : Squaring / Square Roots / Radicals

Simplify the exponent,

.

Possible Answers:

Correct answer:

Explanation:

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:

Explanation:

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 #22 : 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:

Explanation:

A problem like this can be solved similarly to a linear binomial like /

Example Question #23 : 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 equations simplifies into ?

Possible Answers:

Correct answer:

Explanation:

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

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