Polar Coordinates and Polar Form of Complex Numbers Review, Complex Numbers in Polar Form - Products, Quotients and Converting

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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?

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


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