MA 441 | Activity – Chapters 7-9 (Complex Numbers in Polar Form)

TRIPLE DAMAGEQuadrants(15 secs)

100

In which quadrant is θ if

z=-4-4i

?

Quadrant 3

 (a,b)->(-4,-4)

200

In which quadrant is θ if

z=4\sqrt3-4i

?

Quadrant 4

 (a,b)->(4\sqrt3,-4)

300

In which quadrant is θ if

z=-1/4 + (i\sqrt3)/4

?

Quadrant 2

 (a,b)->(-1/4,\sqrt3/4)

DOUBLE DAMAGEUnit CircleCoordinates(30 secs)

100

The coordinates at 30° are

 (\sqrt3/2,1/2) 

200

The coordinates at 90° are

 (0,1) 

300

The coordinates at -45° are

(\sqrt2/2,-\sqrt2/2)

400

The coordinates at

(4\pi)/3

are

(-1/2,-\sqrt 3/2)

500

The coordinates at

(4\pi)/6

are

(-1/2, \sqrt3/2)

DOUBLE DAMAGEθ-Builds(15 secs)

100

\theta=tan^-1((-4)/-4)

matches to which what θ-build?

45°

200

\theta=tan^-1((4)/0)

matches to which what θ-build?

90°

300

\theta=tan^-1((-4)/(4\sqrt3))

matches to which what θ-build?

30°

400

\theta=tan^-1((0)/-4)

matches to which what θ-build?

180°

500

\theta=tan^-1((\sqrt3/4)/(-1/4))

matches to which what θ-build?

60°

Modulus (r)(1 min)

100

Find

r=\sqrt(a^2+b^2)

if 

z=-4-4i

r=\sqrt(32)=4\sqrt2

200

Find

r=\sqrt(a^2+b^2)

if 

z=4\sqrt3-4i

r=\sqrt(64)=8

300

Find

r=\sqrt(a^2+b^2)

if 

z=-1/4+(i\sqrt3)/4

r=\sqrt(1/4)=\sqrt(1)/\sqrt(4)=1/2

400

Find

r=\sqrt(a^2+b^2)

if 

z=4i

r=\sqrt(16)=4

500

Find

r=\sqrt(a^2+b^2)

if 

z=-4

r=\sqrt(16)=4

Argument(1 min)

100

Find

\theta=tan^-1(b/a)

if 

z=-4-4i

\theta=tan^-1((-4)/-4)

θ = 45°-build in Q3

θ = 225°

200

Find

\theta=tan^-1(b/a)

if 

z=4\sqrt(3)-4i

\theta=tan^-1((-4)/(4\sqrt3))

θ = 30°-build in Q4

θ = 330°

300

Find

\theta=tan^-1(b/a)

if 

z=-1/4+(i\sqrt3)/4

\theta=tan^-1((\sqrt3/4)/(-1/4))

θ = 60°-build in Q2

θ = 120°

400

Find

\theta=tan^-1(b/a)

if 

z=4i

\theta=tan^-1(4/0)

 (0,b) 

θ = 90°

500

Find

\theta=tan^-1(b/a)

if 

z=-4

\theta=tan^-1(0/-4)

(-a,0)

θ = 180°

DOUBLE REWARDPolar to Rectangular(1 min)

100

Convert to rectangular form:

z=\sqrt2[cos(45°)+isin(45°)]

z=\sqrt2[\sqrt2/2 + \sqrt2/2i]=1+i

200

Convert to rectangular form:

z=-[cos((4pi)/2)+isin((4pi)/2)]

z=-1[1 + 0i]=-1+0=-1

300

Convert to rectangular form:

z=2/3[cos((7pi)/6)+isin((7pi)/6)]

z=2/3[-\sqrt3/2 - 1/2i]=-\sqrt3/3 -1/3i