Combining Complex Numbers

Front

Define 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, defined as the square root of -1.

Front

What is the imaginary unit 'i'?

Back

Front

How do you add two complex numbers?

Back

To add two complex numbers, add their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

Simplify the expression: (10 + 15i) - (48 - 30i)

Back

-38 + 45i.

Front

What is the formula for squaring a complex number?

Back

The formula for squaring a complex number (a + bi) is (a + bi)^2 = a^2 + 2abi + (bi)^2 = a^2 - b^2 + 2abi.

Front

Calculate: (1 - 7i)^2

Back

-48 - 14i.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi^2 = (ac - bd) + (ad + bc)i.

Front

Calculate the product: 4i(-2 - 8i)

Back

32 - 8i.

Front

What is the result of multiplying two imaginary numbers?

Back

The product of two imaginary numbers (bi)(di) = bdi^2 = -bd, which is a real number.

Front

Calculate: (2i)(3i)

Back

-6.