Complex Numbers

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Define a complex number.

Back

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, defined as i² = -1.

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What is the imaginary unit?

Back

The imaginary unit, denoted as i, is defined as the square root of -1, i.e., i = √(-1).

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How do you add two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, subtract their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

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What is the product of two complex conjugates?

Back

The product of two complex conjugates (a + bi)(a - bi) is a² + b², which is a real number.

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13 - 84i.

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1 + 5i.

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1 + i.

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9 + 6i.

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41.