Imaginary & Complex numbers

Front

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 the value of i^2?

Back

i^2 = -1.

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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

Calculate the product of (4 + 3i) and (4 - 3i).

Back

(4 + 3i)(4 - 3i) = 25.

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CCSS.HSN.CN.C.8

Front

What is the standard form of a complex number?

Back

The standard form of a complex number is a + bi, where a and b are real numbers.

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CCSS.HSN.CN.A.1

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 the formula |a + bi| = √(a² + b²).

Front

What is the argument of a complex number?

Back

The argument of a complex number a + bi is the angle θ formed with the positive x-axis, calculated as θ = arctan(b/a).

Front

What is the result of multiplying a complex number by its conjugate?

Back

The result of multiplying a complex number a + bi by its conjugate a - bi is a² + b².