Operations on 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 is the imaginary unit 'i'?

Back

The imaginary unit 'i' is defined as i = √(-1). It is used to represent the square root of negative numbers.

Front

What is the product of two imaginary numbers, (-6i)(3i)?

Back

The product is 18.

Front

How do you simplify i^24?

Back

i^24 simplifies to 1.

Front

What is the result of multiplying two complex numbers, (-3 + 2i)(1 - 4i)?

Back

The result is 5 + 14i.

Front

How do you subtract complex numbers, (11 - 7i) - (-3 + 12i)?

Back

The result is 14 - 19i.

Front

What is the result of multiplying a complex number by a real number, 3i(4 - i)?

Back

The result is 3 + 12i.

Front

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

Back

The conjugate is a - bi.

Front

How do you add complex numbers?

Back

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

Front

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

Back

The modulus is √(a² + b²).