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 does i² equal?

Back

i² = -1.

Front

How do you add complex numbers?

Back

To add complex numbers, combine their real parts and their imaginary parts separately. For example, (a + bi) + (c + di) = (a + c) + (b + d)i.

Front

How do you subtract complex numbers?

Back

To subtract complex numbers, subtract their real parts and their imaginary parts separately. For example, (a + bi) - (c + di) = (a - c) + (b - d)i.

Front

What is the product of two complex numbers (1-3i)(2+5i)?

Back

The product is 17 - i.

Front

What is the complex conjugate of a complex number?

Back

The complex conjugate of a complex number a + bi is a - bi. It reflects the number across the real axis in the complex plane.

Front

What is the complex conjugate of 4 - 3i?

Back

The complex conjugate is 4 + 3i.

Front

How do you multiply complex numbers?

Back

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

Front

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

Back

The result is -2 + 6i.