Complex Numbers

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.

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

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

To multiply two complex numbers (a + bi)(c + di), use the distributive property: ac + adi + bci + bdi², and remember that i² = -1.

The result is -34 + 13i.

To simplify √-n, express it as i√n, where n is a positive real number.

The simplified form is 6i√3.

The product is -12 - 6i.

i^7 simplifies to -i.

The modulus is given by |a + bi| = √(a² + b²).