Multiplying Complex Numbers

Front

What is the product of two complex conjugates, (a + bi)(a - bi)?

Back

a^2 + b^2

Front

How do you multiply two complex numbers in the form (a + bi)(c + di)?

Back

Use the distributive property (FOIL): ac + adi + bci + bdi^2, and remember that i^2 = -1.

Front

What is the result of multiplying (5 - i)(5 - i)?

Back

24 - 10i

Front

What is the simplified form of 2i(i - 8)?

Back

-2 - 16i

Front

What is the product of (2i)(3i)?

Back

-6

Front

How do you simplify the expression (7 - 5i)(7 + 5i)?

Back

The result is 74.

Front

What is the result of multiplying (-3 - i)(6 - i)?

Back

-19 - 3i

Front

What is the definition of a complex number?

Back

A complex number is a number of 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.

Front

What is the geometric interpretation of complex numbers?

Back

Complex numbers can be represented as points or vectors in a two-dimensional plane, known as the complex plane.