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 i² = -1.

Front

What is the imaginary unit 'i'?

Back

Front

How do you add two complex numbers?

Back

To add two complex numbers, combine 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 (18 - 3i) + ( - 2 -5i)?

Back

The result is 16 - 8i.

Front

How do you simplify (3 + 2i) + (4i + 6)?

Back

Combine like terms: (3 + 6) + (2i + 4i) = 9 + 6i.

Front

What is the product of (7-5i)(7+5i)?

Back

The product is 74.

Front

How do you multiply two complex numbers?

Back

To multiply two complex numbers, use the distributive property (FOIL method): (a + bi)(c + di) = ac + adi + bci + bdi².

Front

What is the result of (5-i)(5-i)?

Back

The result is 24 - 10i.

Front

How do you simplify the expression (-2 + 7i)(4 - 2i)?

Back

The result is 6 + 32i.

Front

What is the conjugate of a complex number a + bi?

Back

The conjugate of a complex number a + bi is a - bi.