Complex Numbers

Front

What is a complex number?

Back

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers, and i is the imaginary unit, defined as √-1.

Front

What is the imaginary unit 'i'?

Back

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

Front

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

Back

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

Front

What is the conjugate of 5 - 2i?

Back

5 + 2i.

Front

How do you add two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately.

Front

Simplify: (8 + 2i) + (-2 - 3i)

Back

6 - i.

Front

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

Back

The modulus of a complex number a + bi is given by √(a² + b²).

Front

What is the argument of a complex number?

Back

The argument of a complex number is the angle θ formed with the positive x-axis in the complex plane, often calculated using tan(θ) = b/a.

Front

What is i^2?

Back

i^2 = -1.

Front

Simplify: i^72

Back

1.