Operations on COmplex Numbers

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 is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is obtained by changing the sign of the imaginary part.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers (a + bi) and (c + di), use the distributive property: (a + bi)(c + di) = ac + adi + bci + bdi^2. Remember that i^2 = -1.

Front

What is the result of multiplying (3 + 2i) and (1 - 4i)?

Back

(3 + 2i)(1 - 4i) = 3 - 12i + 2i - 8i^2 = 3 - 10i + 8 = 11 - 10i.

Front

How do you divide complex numbers?

Back

To divide complex numbers (a + bi) by (c + di), multiply the numerator and denominator by the conjugate of the denominator: (a + bi)/(c + di) * (c - di)/(c - di).

Front

What is the simplified form of i^2?

Back

i^2 = -1.

Front

What is the simplified form of √(-1)?

Back

√(-1) = i.

Front

What is the simplified form of √(-28)?

Back

√(-28) = √(28) * √(-1) = 2i√7.

Front

What are like terms in complex numbers?

Back

Like terms in complex numbers have the same variable at the same power, such as 3i and 5i.

Front

What is the result of (2 + 3i) + (4 - 5i)?

Back

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