Imaginary & Complex numbers

Front

What is an imaginary number?

Back

An imaginary number is a number that can be written as a real number multiplied by the imaginary unit 'i', where i is defined as the square root of -1.

Front

What is the value of i^2?

Back

i^2 = -1.

Front

What is the conjugate of a complex number?

Back

The conjugate of a complex number a + bi is a - bi.

Front

Calculate the product of (4 + 3i) and (4 - 3i).

Back

(4 + 3i)(4 - 3i) = 25.

Front

What is the standard form of a complex number?

Back

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

Front

How do you add two complex numbers?

Back

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

Front

How do you subtract two complex numbers?

Back

To subtract two complex numbers, subtract their real parts and their imaginary parts separately.

Front

What is the modulus of a complex number?

Back

The modulus of a complex number a + bi is given by the formula |a + bi| = √(a² + b²).

Front

What is the argument of a complex number?

Back

The argument of a complex number a + bi is the angle θ formed with the positive x-axis, calculated as θ = arctan(b/a).

Front

What is the result of multiplying a complex number by its conjugate?

Back

The result of multiplying a complex number a + bi by its conjugate a - bi is a² + b².