Complex numbers: Powers of "i"

Front

What is the definition of 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 i = √(-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 value of i^2?

Back

i^2 = -1.

Front

What is the value of i^3?

Back

i^3 = i^2 * i = -1 * i = -i.

Front

What is the value of i^4?

Back

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

Front

What is the pattern in the powers of 'i'?

Back

The powers of 'i' cycle every four: i^1 = i, i^2 = -1, i^3 = -i, i^4 = 1, and then it repeats.

Front

Calculate: i + 2i

Back

3i.

Front

Calculate: 5i - 3i

Back

2i.

Front

What is the result of (3 - i) - (2 + 4i)?

Back

1 - 5i.

Front

What is the result of 5i + i?

Back

6i.