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 (∛). For example, √4 = 2.

Front

What is a rational exponent?

Back

A rational exponent is an exponent that is a fraction. For example, x^(1/2) is equivalent to √x.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1, i.e., i^2 = -1.

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately. For example, (2 + 3i) + (4 + 5i) = (2 + 4) + (3i + 5i) = 6 + 8i.

Front

What is the result of i^4?

Back

i^4 = 1, because (i^2)^2 = (-1)^2 = 1.

Front

How do you multiply complex numbers?

Back

To multiply complex numbers, use the distributive property (FOIL). For example, (a + bi)(c + di) = ac + adi + bci + bdi^2.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used to simplify division of complex numbers.

Front

What is the result of (2 + 3i)^2?

Back

(2 + 3i)^2 = 4 + 12i + 9i^2 = 4 + 12i - 9 = -5 + 12i.

Front

What is the simplified form of √(a^2)?

Back

The simplified form of √(a^2) is |a|, the absolute value of a.

Front

What is the value of i^66?

Back

i^66 = -1, because i^66 can be simplified using the cycle of i (i, -1, -i, 1).