Operations with Complex Numbers Practice

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 i^2 = -1.

Front

How do you add complex numbers?

Back

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

Front

How do you subtract complex numbers?

Back

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

Front

What is the product of two complex numbers?

Back

The product of two complex numbers (a + bi)(c + di) is given by ac + adi + bci + bdi^2, which simplifies to (ac - bd) + (ad + bc)i.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used to simplify division of complex numbers.

Front

How do you multiply a complex number by a real number?

Back

To multiply a complex number by a real number, multiply both the real and imaginary parts by that number. For example, k(a + bi) = ka + kbi.

Front

What is the square of a complex number?

Back

The square of a complex number (a + bi)^2 is a^2 + 2abi + (bi)^2, which simplifies to (a^2 - b^2) + 2abi.

Front

What is the result of (4i)^2?

Back

(4i)^2 = 16i^2 = 16(-1) = -16.

Front

How do you simplify the expression (8 + 9i) + (4 - 6i)?

Back

Combine the real parts and the imaginary parts: (8 + 4) + (9 - 6)i = 12 + 3i.

Front

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

Back

3i(3i - 4) = 9i^2 - 12i = -9 - 12i.