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

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

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

Back

The result is -2 + 6i.

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?

Back

To multiply complex numbers, use the distributive property (FOIL method). For example, (a + bi)(c + di) = ac + adi + bci + bdi², and since i² = -1, simplify accordingly.

Front

What is the result of (4 – 3i)(-7 – 2i)?

Back

The result is -34 + 13i.

Front

What is the square of the imaginary unit 'i'?

Back

The square of the imaginary unit 'i' is i² = -1.

Front

What is the result of (2i)(3i)?

Back

The result is -6.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi. It is used in division and to find the modulus.