Pure Imaginary Numbers and Simplifying Radicals

Front

What is a pure imaginary number?

Back

A pure imaginary number is a complex number that can be written in the form bi, where b is a real number and i is the imaginary unit, defined as the square root of -1.

Tags

CCSS.HSN.CN.A.1

Front

How do you simplify the square root of a negative number?

Back

To simplify the square root of a negative number, factor out -1 from the radicand. For example, √-a = √(-1) * √a = i√a.

Front

What is the value of i^2?

Back

The value of i^2 is -1.

Tags

CCSS.HSN.CN.A.1

Front

What is the pattern for powers of i?

Back

The powers of i cycle every four: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1, and then it repeats.

Tags

CCSS.HSN.CN.A.2

Front

How do you simplify √-28?

Back

√-28 can be simplified by factoring out -1: √-28 = √(-1) * √28 = i√28 = 2i√7.

Front

What is the simplified form of √150?

Back

The simplified form of √150 is √(25 * 6) = √25 * √6 = 5√6.

Front

What is the value of i^13?

Back

To find i^13, reduce the exponent modulo 4: 13 mod 4 = 1, so i^13 = i.

Tags

CCSS.HSN.CN.A.2

Front

How do you simplify 2√-32?

Back

2√-32 = 2√(-1) * √32 = 2i * √32 = 2i * √(16 * 2) = 2i * 4√2 = 8i√2.

Front

What is the relationship between complex numbers and the Cartesian plane?

Back

Complex numbers can be represented on the Cartesian plane, where the x-axis represents the real part and the y-axis represents the imaginary part.

Tags

CCSS.HSN.CN.B.4

Front

What is the conjugate of a complex number?

Back

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

Tags

CCSS.HSN.CN.A.3