Imaginary Numbers

Front

What letter usually represents an imaginary number?

Back

i

Front

What is the definition of 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

-1

Front

What is the standard form of a complex number?

Back

A complex number is expressed in the form a + bi, where a is the real part and b is the imaginary part.

Front

What is the real part of the complex number 3 + 4i?

Back

3

Front

What is the imaginary part of the complex number 3 + 4i?

Back

4

Front

How do you add two complex numbers, (2 + 3i) and (4 + 5i)?

Back

(2 + 3i) + (4 + 5i) = (2 + 4) + (3 + 5)i = 6 + 8i.

Front

How do you multiply two complex numbers, (1 + 2i) and (3 + 4i)?

Back

(1 + 2i)(3 + 4i) = 3 + 4i + 6i + 8i^2 = 3 + 10i - 8 = -5 + 10i.

Front

What is the conjugate of the complex number 5 - 2i?

Back

The conjugate is 5 + 2i.

Front

What is the modulus of the complex number 3 + 4i?

Back

The modulus is √(3^2 + 4^2) = √(9 + 16) = √25 = 5.