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 does i^2 equal?

Back

i^2 = -1.

Front

Simplify: 3i - (4 + 7i)

Back

-4 - 4i.

Front

Multiply: (7 + 2i)(9 - 6i)

Back

75 - 24i.

Front

What is the real part of the complex number 4 + 3i?

Back

The real part is 4.

Front

What is the imaginary part of the complex number 4 + 3i?

Back

The imaginary part is 3.

Front

How do you add complex numbers?

Back

To add complex numbers, add their real parts and their imaginary parts separately.

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract their real parts and their 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).