Flashcardizz 3.2_Complex Number

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, defined as the square root of -1.

Front

What does the imaginary unit 'i' represent?

Back

The imaginary unit 'i' represents the square root of -1, which is a fundamental concept in complex numbers.

Front

What is the value of i^2?

Back

i^2 = -1.

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

How do you subtract two complex numbers?

Back

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

Front

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

Back

The product is given by (ac - bd) + (ad + bc)i.

Front

How do you simplify the expression (10 + 15i) - (48 - 30i)?

Back

The simplified form is -38 + 45i.

Front

What is the result of multiplying (-6i)(-6 - 2i) + (3i)(8 + 4i)?

Back

The result is -24 + 60i.

Front

How do you add the complex numbers (-7 + 16i) and (-18 + 13i)?

Back

The sum is -25 + 29i.

Front

What is the simplified form of \sqrt{-64} + \sqrt{-9} - \sqrt{-25}?

Back

The simplified form is 6i.