Imaginary and Complex Numbers

What is an imaginary number?

• A number that cannot be used in mathematical calculations

• A complex number that can be written as a real number multiplied by the imaginary unit i.

• A number that doesn't exist in the real world

• A number with no value

Answer explanation

An imaginary number is a complex number that can be expressed as a real number multiplied by the imaginary unit i.

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What is a complex number?

• A number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit.

• A number that can only be expressed in the form a - bi

• A number that has no real part

• A number that can only be expressed in the form a + bi

Answer explanation

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit. This choice correctly defines a complex number.

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CCSS.HSN.CN.A.1

Simplify the expression: √(-16)

• 4i

• 16

• -4

• 0

Answer explanation

The square root of a negative number is not a real number. It is represented by the imaginary unit 'i'. Therefore, the simplified expression is 4i, which is the correct choice.

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What is the value of i^2?

• 1

• 2

• 0

• -1

Answer explanation

The value of i^2 is -1 because i is defined as the square root of -1.

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Add (3 + 2i) + (4 - 5i) and write the answer in a + bi form.

• 9 - 2i

• 2 - 3i

• 7 - 3i

• 5 + 7i

Answer explanation

To add complex numbers, add the real parts and the imaginary parts separately. (3 + 2i) + (4 - 5i) = (3 + 4) + (2 - 5)i = 7 - 3i. Therefore, the correct answer is 7 - 3i.

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Subtract (5 - 3i) - (2 + 4i) and write the answer in a + bi form.

• 2 - 7i

• 4 - 5i

• 3 - 7i

• 8 - 1i

Answer explanation

To subtract complex numbers, subtract the real parts and the imaginary parts separately. (5 - 3i) - (2 + 4i) = (5 - 2) + (-3 - (-4))i = 3 - 7i. Therefore, the correct answer is 3 - 7i.

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Perform the operation (3 + 2i) * (4 - 5i) and write the answer in a + bi form.

• 15 + 3i

• 20 - 10i

• 22 - 7i

• 12 - 7i

Answer explanation

To multiply complex numbers, use the FOIL method. The correct answer is 22 - 7i, which is obtained by multiplying the real parts (3 * 4) and the imaginary parts (-2 * -5) separately and then combining them.

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If z = 2 + 3i and w = 4 - 2i, find z + w and write the answer in a + bi form.

• 6 + i

• 2 - 5i

• 10 + 3i

• 8 - i

Answer explanation

To find z + w, add the real parts and the imaginary parts separately. The real part is 2 + 4 = 6, and the imaginary part is 3 - 2 = 1. Therefore, z + w = 6 + 1i. This matches the correct choice 6 + i.

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If a = 1 + 2i and b = 3 - 4i, find a + b and write the answer in a + bi form.

• 4 - 2i

• 2 - 6i

• 4 - 6i

• 2 - 2i

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What is the value of i^3?

• 1

• i

• -1

• -i

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