Imaginary/Complex Operations

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 the square root of -1.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

Simplify: i^4

Back

i^4 = 1.

Front

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

Back

The conjugate is a - bi.

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 modulus of a complex number a + bi?

Back

The modulus is |a + bi| = √(a^2 + b^2).

Front

Simplify: (2 + 3i)(4 - 2i)

Back

(2 + 3i)(4 - 2i) = 14 + 8i.

Front

What does the letter 'i' represent in complex numbers?

Back

The letter 'i' represents the imaginary unit, which is the square root of -1.

Front

What is the result of i^6?

Back

i^6 = -i.

Front

What is the sum of (3 + 2i) and (1 - 4i)?

Back

(3 + 2i) + (1 - 4i) = 4 - 2i.