Unit 6 Radicals and Imaginary Numbers

Front

What is a radical in mathematics?

Back

A radical is an expression that includes a root, such as a square root or cube root. For example, √4 is a radical.

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 √-1.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

How do you simplify √-a?

Back

√-a can be simplified to i√a.

Front

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

Back

The result is (a + c) + (b + d)i.

Front

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

Back

The result is (a - c) + (b - d)i.

Front

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

Back

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

Front

What is the result of √-4 + √-9?

Back

The result is 2i + 3i = 5i, which is imaginary.