Complex Conjugates

Front

What is a complex conjugate?

Back

The complex conjugate of a complex number a + bi is a - bi, where a and b are real numbers.

Front

What is the complex conjugate of 3 - 2i?

Back

3 + 2i

Front

What is the complex conjugate of 5i?

Back

-5i

Front

What is the complex conjugate of -7i?

Back

7i

Front

What is the complex conjugate of 5 + 7i?

Back

5 - 7i

Front

What is the complex conjugate of 2 - 3i?

Back

2 + 3i

Front

If z = a + bi, what is the formula for its complex conjugate?

Back

z* = a - bi

Front

How do you find the complex conjugate of a real number?

Back

The complex conjugate of a real number a is simply a, since there is no imaginary part.

Front

What happens when you multiply a complex number by its conjugate?

Back

The result is a real number: (a + bi)(a - bi) = a^2 + b^2.

Front

What is the geometric interpretation of complex conjugates?

Back

Complex conjugates are reflections of each other across the real axis in the complex plane.