Simplify Radicals and Imaginary Numbers Review Alg.2

Front

What is a radical?

Back

A radical is an expression that includes a root, such as a square root (√) or cube root (∛).

Front

How do you simplify √(a*b)?

Back

√(a*b) = √a * √b, provided a and b are non-negative.

Front

What is the value of √(x^2)?

Back

The value of √(x^2) is |x|, the absolute value of x.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as √(-1).

Front

How do you simplify -√-a?

Back

-√-a = -i√a, where a is a positive real number.

Front

What is the result of i^2?

Back

i^2 = -1.

Front

What is the pattern of powers of 'i'?

Back

The powers of 'i' cycle every four: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1.

Front

How do you multiply two complex numbers (a + bi)(c + di)?

Back

(a + bi)(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i.

Front

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

Back

The conjugate is a - bi.

Front

How do you divide complex numbers (a + bi) / (c + di)?

Back

Multiply numerator and denominator by the conjugate of the denominator: (a + bi)(c - di) / (c + di)(c - di).