Imaginary Numbers

Front

What is an imaginary number?

Back

An imaginary number is a 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

Simplify: √(-36)

Back

± 6i.

Front

What is the result of adding two imaginary numbers?

Back

The result is another imaginary number, which can also be expressed in the form a + bi, where a and b are real numbers.

Front

Simplify: -3i(4 + 2i)

Back

6 - 12i.

Front

What is the product of two imaginary numbers?

Back

The product of two imaginary numbers is a real number. For example, (ai)(bi) = -ab.

Front

Simplify: (2 - 4i) + (5 + 6i)

Back

7 + 2i.

Front

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

Back

The conjugate is a - bi.

Front

Simplify: 2i√8

Back

± 4i√2.

Front

What is the sum of a real number and an imaginary number?

Back

The sum is a complex number in the form a + bi.