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ACT Math : How to subtract complex numbers

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Example Questions

Example Question #1 : Complex Numbers

Subtract from , given:

a = 3 + i

b = 4 - 2i

Possible Answers:

-1 - 3i

1 - 3i

3 + i

-1 + 3i

1+ 3i

Correct answer:

1 - 3i

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 b - a ,

$b-a = \left ( 4-2i\right ) - \left ( 3 + i\right ) = \left ( 4-3\right ) + i\left ( -2-1\right ) = 1 - 3i$

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Example Question #1 : Complex Numbers

Simplify the exponent,

$(3^{6})^{2}$ .

Possible Answers:

$3^{3}$

$3^{12}$

$3^{8}$

$3^{4}$

Correct answer:

$3^{12}$

Explanation:

When you have an exponent on the outside of parentheses while another is on the inside of the parentheses, such as in $(3^{6})^{2}$ , multiply the exponents together to get the answer: $3^{12}$ .

This is different than when you have two numbers with the same base multiplied together, such as in $x^{2} \cdot x^{3} = x^{5}$ . In that case, you add the exponents together.

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Example Question #3 : Complex Numbers

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

Simplify:

(2-2i) - (4-i)

Possible Answers:

6-i

-2-i

6-3i

$\textup{None of these}$

-2-3i

Correct answer:

-2-i

Explanation:

Solving this equation is very similar to solving a linear binomial like (a+bx) . To solve, just combine like terms, being careful to watch for double negatives.

(2-2i) - (4-i)

(2-4) + (-2i-(-i))

-2 -(-2i+i)

-2 -i

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Example Question #4 : Complex Numbers

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:

-(4-i) = (4-i) = 0

2i - (2-2i) = -2 +4i

-3i - (7-7i) = -7 +4i

(7-i) -(2+i) = 5-2i

7i- (3-i) = 3-8i

Correct answer:

7i- (3-i) = 3-8i

Explanation:

A problem like this can be solved similarly to a linear binomial like (a +bx) /

7i - (3-i) = 3-8i

7i + (-3 + i) = 3-8i

$-3 +8i \neq 3+8i$

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Example Question #5 : Complex Numbers

Complex numbers take the form a+bi , 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 4+2i ?

Possible Answers:

(0 + 7i) - (-4 - 5i)

3 - (7 + 2i)

(8-5i) + (-4 +7i)

(10 -i) - (6 - i)

0+ 6i + (-4 - 4i)

Correct answer:

(8-5i) + (-4 +7i)

Explanation:

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

(8-5i) + (-4 +7i)

(8-4) + (-5i + 7i)

4 + 2i

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ACT Math : How to subtract complex numbers

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

Example Question #1 : Complex Numbers

Example Question #1 : Complex Numbers

Example Question #3 : Complex Numbers

Example Question #4 : Complex Numbers

Example Question #5 : Complex Numbers

All ACT Math Resources

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