1. Polar Coordinates z=rcisӨ
Write z=2+3i in polar form.
1: sketch the point.
2. find modulus & argument (angle the line makes with the real axis)
Modulus is √(22+32)=√13
Ө=tan-1(3/2)=0.9828rad (4dp)
2+3i=√13cos √13isin0.983 = √13(cos isin0.983)
3. write in polar (rcisӨ) form.
= √13cis0.9828

2. Polar Form rcisθ=r(cos θ+isin θ)
r=√ (a2+b2)
r=√ ( )
r=3.32 90 θ
0.9
Θ=inv.tan(3.2/0.9)
=74.29’
=3.2cos
3.2
Θ= --( )
Θ= ’ i
(rectangular form)
Polar form is 3.32cis( ’)

3. On GRAPHICS CALCULATOR:
RUN mode->OPTN->CPLX,
To find modulus: Abs(2+3i)
To find argument: Arg (2+3i)

4. Practice: write in polar form (with arguments in radians)
Z=6+i
Z=-4+2i
Z=-3-4i
Z=2-5i
Answers:
a)z=6.08cis(0.1651)
b)z=4.47cis(2.6779)
c)z=5cis( )
c)z=5.39cis( )

5. Converting from polar to rectangular form… expand out:
Write z=3cis(-150°) in rectangular form.
3cis(-150)=3(cos-150+isin-150)
= i
Change to rectangular form:
Z=4cis(27°)
Z=2.3cis(140°)
Z=1.9cis(-1.427rad)
Z=5.4cis(-2.15rad)
Ex 32.1 p.293 #2-5

6. Operating on Numbers in Polar Form
Multiplication: multiply the moduli, add the argument.
Division: divide the moduli, subtract the argument.
Raising to a power
(This is called DeMoivre’s Theorem)
Ex 32.2 p.293
Ex 32.3 p.296 #1