Complex Numbers Review

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 imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, which means i^2 = -1.

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CCSS.HSN.CN.A.1

Front

How do you simplify the expression 2i - 7i + 10?

Back

The expression simplifies to -5i + 10.

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CCSS.HSN.CN.A.2

Front

What is the result of multiplying (2i)(3i)?

Back

The result is -6, since (2i)(3i) = 6i^2 = 6(-1) = -6.

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CCSS.HSN.CN.A.2

Front

What is the product of (-3i)(4i)(-5i)?

Back

The product is -60i.

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CCSS.HSN.CN.A.2

Front

What is the standard form of a complex number?

Back

The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part.

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CCSS.HSN.CN.A.1

Front

How do you add complex numbers?

Back

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

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CCSS.7.NS.A.1C

Front

How do you subtract complex numbers?

Back

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

Front

What is the conjugate of a complex number a + bi?

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 multiply complex numbers in the form (a + bi)(c + di)?

Back

To multiply complex numbers, use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2, and simplify using i^2 = -1.

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CCSS.HSN.CN.A.2