Complex Numbers

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.

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CCSS.HSN.CN.A.1

Front

What does i^2 equal?

Back

i^2 = -1.

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CCSS.HSN.CN.A.1

Front

How do you add complex numbers?

Back

To add complex numbers, add the real parts and the 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 the real parts and the imaginary parts separately.

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CCSS.HSN.CN.A.1

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL) and apply the fact that i^2 = -1.

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CCSS.HSN.CN.A.2

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 divide complex numbers?

Back

To divide complex numbers, multiply the numerator and denominator by the conjugate of the denominator.

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CCSS.HSN.CN.A.3

Front

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

Back

The modulus of a complex number a + bi is given by √(a^2 + b^2).

Front

What is the argument of a complex number?

Back

The argument of a complex number is the angle θ in polar coordinates, given by θ = arctan(b/a).