Imaginary Numbers

Front

What is an imaginary number?

Back

An imaginary number is a complex 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

How do you express the square root of a negative number?

Back

The square root of a negative number can be expressed using imaginary numbers. For example, √(-a) = i√a.

Front

What is the result of i^3?

Back

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

Front

What is the result of i^4?

Back

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

Front

How do you simplify i^n for n > 4?

Back

To simplify i^n for n > 4, find the remainder of n when divided by 4. The results are: 0 (1), 1 (i), 2 (-1), 3 (-i).

Front

What is the principal square root of -64?

Back

The principal square root of -64 is 8i.

Front

What is the result of 5 times the square root of -49?

Back

5 times the square root of -49 is 35i.

Front

What is the value of i^9?

Back

i^9 = i.

Front

What is the relationship between real numbers and imaginary numbers?

Back

Real numbers are a subset of complex numbers, which can be expressed as a + bi, where a is the real part and b is the imaginary part.