Imaginary Numbers

Front

What are 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 i^2?

Back

i^2 = -1.

Front

How do you solve the equation 5m^2 + 1 = 6?

Back

Subtract 1 from both sides to get 5m^2 = 5, then divide by 5 to get m^2 = 1. Taking the square root gives m = ±1.

Front

What is the result of i^4?

Back

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

Front

What is the principal square root of -9?

Back

The principal square root of -9 is 3i.

Front

How do you simplify the expression i^79?

Back

i^79 can be simplified by finding the remainder of 79 divided by 4. Since 79 mod 4 = 3, i^79 = i^3 = -i.

Front

What is the solution to the equation x^2 + 8 = 28?

Back

Subtract 8 from both sides to get x^2 = 20. Taking the square root gives x = ±2√5.

Front

What is the solution to the equation -3x^2 = -63?

Back

Divide both sides by -3 to get x^2 = 21. Taking the square root gives x = ±√21.

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.

Front

What is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as the square root of -1.