FLASHCARD REVIEW - Operations with 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 i² = -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

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 result of (7 + 2i) - (-12 - 4i)?

Back

The result is 19 + 6i.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL). For example, (a + bi)(c + di) = ac + adi + bci + bdi² = (ac - bd) + (ad + bc)i.

Front

What is the result of (5 - i)²?

Back

The result is 24 - 10i.

Front

How do you divide two complex numbers?

Back

To divide two complex numbers, multiply the numerator and denominator by the conjugate of the denominator. For example, to divide (a + bi) by (c + di), multiply by (c - di).

Front

Back

Front

How do you simplify the expression (9 + 2i) - 7i + 1?

Back

The simplified result is 10 - 5i.