Imaginary Solutions

Front

Define 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 square root of a negative number?

Back

The square root of a negative number is an imaginary number. For example, √-x = i√x.

Front

Solve: x² = -25

Back

x = ±5i

Front

What is the principal square root of -1?

Back

The principal square root of -1 is i.

Front

Solve: x² = -64

Back

x = ±8i

Front

What is the relationship between real numbers and imaginary numbers?

Back

Real numbers are on the number line, while imaginary numbers are on a perpendicular axis, forming the complex plane.

Front

Solve: x² = -49

Back

x = ±7i

Front

What is the standard form of a complex number?

Back

The standard form of a complex number is a + bi, where a is the real part and b is the imaginary part.

Front

Solve: x² = -16

Back

x = ±4i

Front

What does 'i' represent in complex numbers?

Back

'i' represents the imaginary unit, defined as √-1.