Radicals, Rational Exponents, Complex Numbers

Front

What is a radical?

Back

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

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction, representing both a power and a root. For example, x^(1/n) is the nth root of x.

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 i^2?

Back

i^2 = -1.

Front

What is the result of (a + bi)(c + di)?

Back

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

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

What is the conjugate of a complex number?

Back

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

Front

How do you multiply complex numbers?

Back

Multiply complex numbers using the distributive property and combine like terms. For example, (a + bi)(c + di) = ac + adi + bci + bd(-1).

Front

What is the process to rationalize the denominator?

Back

To rationalize the denominator, multiply the numerator and denominator by a suitable expression that eliminates the radical in the denominator.

Front

What is the value of i^4?

Back

i^4 = 1.