Imaginary and Complex Numbers

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What is an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

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CCSS.HSN.CN.A.1

Front

What is 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.

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CCSS.HSN.CN.A.1

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi.

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CCSS.HSN.CN.A.3

Front

How do you add two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately.

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CCSS.7.NS.A.1C

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, subtract their real parts and their imaginary parts separately.

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CCSS.HSN.CN.A.2

Front

What is the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by √(a² + b²).

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers (a + bi)(c + di), use the distributive property and combine like terms: (ac - bd) + (ad + bc)i.

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CCSS.HSN.CN.A.2

Front

What is the result of multiplying (2-5i)(2+5i)?

Back

The result is 29.

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CCSS.HSN.CN.C.8

Front

What is the result of adding (2 - 4i) + (5 + 7i)?

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The result is 7 + 3i.

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CCSS.HSN.CN.A.2

Front

How many roots does the equation y = x² + 2x - 3 have?

Back

The equation has two roots.