Polar form of complex numbers

Polar form of complex numbers

Knowing the argument and the modulus of a complex number allows us to convert a complex number from its rectangular form, which is what we have been using thus far, to its other basic form – polar form. We will see that while a complex number in rectangular form is denoted by its horizontal and vertical components, a complex number in polar form is denoted by its magnitude and argument.

Lessons

  • 1.
    Convert the following complex numbers from rectangular form to polar form
    a)
    z=2i3 z=2i-3

    b)
    w=53iw=-5-3i

    c)
    z=4i z=4-i


  • 2.
    Convert the following complex numbers from polar form to rectangular form
    a)
    z=4(cos(π4)+isin(π4)) z=4(\cos(\frac{\pi}{4})+i\sin(\frac{\pi}{4}))

    b)
    w=13(cos(180)+isin(180)) w=13(\cos(180^{\circ})+i\sin(180^{\circ}))

    c)
    z=4(cos(5π3)+isin(5π3)) z=4(\cos(\frac{5\pi}{3})+i\sin(\frac{5\pi}{3}))


  • 3.
    Given that z=43iz=4-3i , and w=2iw=2-i, find z+wz+w and express it in polar form