imaginary numbers

Front

Define imaginary numbers.

Back

Imaginary numbers are numbers 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 i²?

Back

i² = -1.

Front

Solve: x² = -16.

Back

x = ± 4i.

Front

What is the principal square root of -1?

Back

The principal square root of -1 is i.

Front

Simplify: √-25.

Back

√-25 = 5i.

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 line, forming the complex plane.

Front

Solve: x² = -49.

Back

x = ± 7i.

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.

Front

Simplify: √-36.

Back

√-36 = 6i.

Front

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

Back

The conjugate is a - bi.