Polar Form
Definition
Definition
So far, we have written complex numbers in the rectangular form : z = a + bi.
So far, we have written complex numbers in the rectangular form : z = a + bi.
They can also be expressed in an equivalent polar form : z = R(cosθ + i sinθ), where R is the modulus and θ is the argument.
They can also be expressed in an equivalent polar form : z = R(cosθ + i sinθ), where R is the modulus and θ is the argument.
This can further be expressed in an equivalent exponential form : z = Reiθ, the relationship between the polar form and exponential form is given by Euler's Formula.
This can further be expressed in an equivalent exponential form : z = Reiθ, the relationship between the polar form and exponential form is given by Euler's Formula.
Try it!
Try it!
Use the applet below to explore the polar form of complex numbers.
Use the applet below to explore the polar form of complex numbers.