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 multiply two imaginary numbers, such as (2i)(3i)?

Back

To multiply two imaginary numbers, multiply the coefficients and apply the property i^2 = -1. For (2i)(3i), the result is 6i^2 = 6(-1) = -6.

Front

What is the sum of two complex numbers, (a + bi) + (c + di)?

Back

The sum is (a + c) + (b + d)i, where a, b, c, and d are real numbers.

Front

What is the result of adding (5-2i) and (-7+8i)?

Back

The result is (-2 + 6i).

Front

How do you simplify the expression 2i - 7i + 10?

Back

Combine like terms: 10 - 5i.

Front

What is the pattern for 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

What is the value of i^79?

Back

i^79 can be simplified using the cycle of powers of i. Since 79 mod 4 = 3, i^79 = i^3 = -i.

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 and i is the imaginary unit.

Front

How do you subtract two complex numbers, such as (a + bi) - (c + di)?

Back

The difference is (a - c) + (b - d)i.