14.4 The exponential form of a complex number
Consider the Maclaurin series for , and . What happens when we add ? Well a fair amount of algebra to start with! After that, however, we do get an interesting result, though.
This means that 44 4 This is sometimes referred to as ”Euler’s formula”
Which provides a link between trigonometry and complex numbers! This turns out to be very useful in proving trig identities.
For any complex number, where is the modulus and is the argument, we have
We can use this to write other complex numbers, such as in the form .