Section 5 Review

Simplify i

100

Simplify 

sqrt(-36)

6i

200

Simplify

i¹²

1

300

-1/2sqrt(-300)

-5sqrt(3)i

400

Simplify

i⁹⁹

-i

500

Simplify

(5i¹⁵)(3i⁷)

-15

Operations

100

Simplify and write in standard Cartesian form (a+bi):

(10+3i)+(5+8i)

15+11i

200

Simplify and write in standard Cartesian form (a+bi):

(-8+5i)-(5-7i)

-13+12i

300

Simplify and write in standard Cartesian form (a+bi):

(5+sqrt(-36))(3-sqrt(-16))

39-2i

400

Simplify and write in standard Cartesian form (a+bi):

1/(2+4i)

1/10-1/5i

500

Simplify and write in standard Cartesian form (a+bi):

(5-3i)/(1-i)

4+i

Polar Form

100

Find the modulus of:

12+13i

sqrt(313)

200

Find the modulus (in simplest form) of:

2sqrt(3)-10i

4sqrt(7)

300

Write (2, 300^o) in standard Cartesian Form.

sqrt(3)-i

400

Write the following in polar form:

-3sqrt(3)-3i

(6, 210^o)

500

Write the following in polar form:

8-8i

(8sqrt(2), 315^o)

Transformations

100

Transform 3+2i by:

Finding its conjugate.  

(State the new complex number and describe the transformation)

3-2i

Reflection over the real axis

200

Transform 3+2i by:

Multiplying by -3  

(State the new complex number and describe the transformation)

-9-6i

Rotation of 180 degree about the origin and a dilation with scale factor 3

300

Transform 3+2i by:

Multiplying by i

(State the new complex number and describe the transformation)

-2+3i

Rotation of 90 degrees about the origin

400

Transform 3+2i by:

Subtracting 4-2i

(State the new complex number and describe the transformation)

-1+4i

Translation of 4 units to the left and 2 units up

500

Transform 3+2i by:

Dividing by i

(State the new complex number and describe the transformation)

2-3i

Rotation of -90 degrees about the origin

Trig Form

100

Write the following in Trigonometric Form:

(2,(4pi)/3)

2(cos((4pi)/3)+isin((4pi)/3))

200

Write the following in Trigonometric Form:

-5i

5(cos270^o+isin270^o)

300

Write the following in Trigonometric Form:

2-2i

2sqrt(2)(cos315^o +isin315^o)

400

Write the following in Trigonometric Form:

-5/2-(5sqrt(3))/2i

5(cos240^o +isin240^o)

500

Write the following in standard Cartesian Form:

9(cos(-(11pi)/2)+isin(-(11pi)/2))

9i

Mult/Div/Power

100

Multiply the following complex numbers. Leave your answer in Trigonometric Form.

z_1=4(cos32^o +isin32^o)

z_2=3(cos61^o +isin61^o)

12(cos93^o +isin93^o)

200

Divide the following complex numbers. Leave your answer in Trigonometric Form.

z_1=12(cos84^o +isin84^o)

z_2=3(cos35^o +isin35^o)

4(cos49^o +isin49^o)

300

Find z⁵  (in Trigonometric Form) if 

z=2(cos24^o +isin24^o)

32(cos120^o +isin120^o)

400

Find z⁴  (in Trigonometric Form) if 

z=2+2i

64(cos180^o +isin180^o)

500

Find z⁶  (in Cartesian Form) if 

z=-1+i

8i