Polar Coordinates and Polar Form of Complex Numbers Review, Complex Numbers in Polar Form - Products, Quotients and Converting
5 cis 21⁰
(10 cis 28⁰) ÷ (2 cis 7⁰)
4 cis 95⁰
(16 cis 125⁰) ÷ (4 cis 30⁰)
6 cis 100⁰
(2 cis 80⁰)(3 cis 20⁰)
5 cis 150⁰
(25 cis 300⁰) ÷ (5 cis 150⁰)
27 cis 360⁰
(3 cis 90⁰)(9 cis 270⁰)
5 cis 40⁰
(5 cis 220⁰) ÷ (1 cis 180⁰)
5 cis 305⁰
(5 cis 300⁰)(1 cis 5⁰)
24 cis 225⁰
(6 cis 25⁰)(4 cis 200⁰)
4 cis 80⁰
24 cis 100⁰) ÷ (6 cis 20⁰)
27 cis 75⁰
9 cis 30⁰)(3 cis 45⁰)
2 cis 240°
Convert to Polar Form: -1 -i√3
4 cis 210⁰
Convert to Polar Form: -2√3-2i
5 cis 135°
Convert to Polar Form: -5√2/2 + 5√2/2i
2√7 cis 30°
Convert to Polar Form: √21 + i√7
2√7 cis 300°
Convert to Polar Form: √7 - i√21
how to convert rectangular to polar
Given x and y, use Pythagorean theorem to find r Use x and y and the inverse tangent to find angle
Even N
Roses with 2n petals
Odd N
Roses with n petals
10√2 cis 135°
Simplify and Convert to Polar Form: (-7 + 2i) + (-3 + 8i)
10 cis 0°
Simplify and Convert to Polar Form: (3 + i)(3 - i)
Convex Limacon
a≥2b
Z=a+bi is the _________ form?
rectangular
θ
tan⁻¹(y/x)
2 cis 90°
Convert to Polar Form: 2i
4 cis 90°
Simplify and Convert to Polar Form: (4 + 2i) + (-4 + 2i)
2√5 cis 0°
Simplify and Convert to Polar Form: (4 + 2i)(4 - 2i)
4√2 cis 45°
Simplify and Convert to Polar Form: (6 - i) - (2 - 5i)
The real part of this complex number is _______?
a
conjugate complex numbers
a+bi ; a-bi
Limacon with an Inner Loop
a<b
Cardioid
a=b
The imaginary part is ______?
b
Dimpled Limacon
b<a≤2b
A _____________ ____________ is an expression of the form a+bi where a and b are real nimbers?
complex number
This is the _________ of complex numbers?
division
The y-axis is called the ________ __________?
imaginary axis
=-1?
i²
The _________ is the distance the complex number is from the origin?
modulus
This is the _________ of complex numbers?
multiplication
z=r(cosθ+isinθ) is the ________form?
polar
Limacons and Cardioids
r=a+bSinθ
Rose Curves
r=aCos(nθ) r=aSin(nθ)
X-Axis Circle
r=aCosθ r=-aCosθ
Y-Axis Circle
r=aSinθ r=-aSinθ
x
rCosθ
y
rSinθ
What is the shorthand for r(cosθ + sinθi), both sin and cos have to match?
rcis(θ)
The x- axis is called the __________ __________?
real axis
Polar Form
z=r(Cosθ+iSinθ)
What is called the modulus (hypotenuse,or absolute value) of a complex number?
|z|
|z| is defined as____________?
√a²+b²
r
√x²+y²
