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.

Front

What does the imaginary unit 'i' represent?

Back

The imaginary unit 'i' represents the square root of -1.

Front

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

Back

7 - 3i

Front

What is the result of (5 - 2i) + (-7 + 8i)?

Back

-2 + 6i

Front

What is i^2 equal to?

Back

-1

Front

What is the result of -6i + 3i?

Back

-3i

Front

How do you add complex numbers?

Back

To add complex numbers, combine the real parts and the imaginary parts separately.

Front

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

Back

The conjugate is a - bi.

Front

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

Back

The modulus is √(a² + b²).

Front

How do you multiply complex numbers (a + bi)(c + di)?

Back

Use the distributive property: ac + adi + bci + bdi², and remember that i² = -1.