Trigonometry PRACTICE Test

Online Homework System Assignment Worksheet

6/21/18 - 4:35 PM

Name: ____________________________ Class: American Public University System - Precalculus (MATH111 C003 Win 18) (3u7gt5)

Class #: ____________________________ Section #: ____________________________ Instructor:Maple T.A. Administrator Assignment:PRACTICE TEST 7.5

Question 1: (1 point)

Find the fourth roots of .

(a)

(b)4

(c)

(d)

(e)

(f) 4

(g)

(h)

(i) 4

Question 2: (1 point)

Find all the cube roots of 8.

(a) (b)

−16i

2(cos( ) + i sin( ))15π8 15π8 (cos( ) + i sin( ))7π8 7π8

2(cos( ) + i sin( ))3π16 3π16 2(cos( ) + i sin( ))3π8 3π8 2(cos( ) + i sin( ))11π16 11π16 (cos( ) + i sin( ))3π8 3π8

2(cos( ) + i sin( ))7π8 7π8 2(cos( ) + i sin( ))11π8 11π8

2 i −1 − i 3‾√ −2 − 2 i 3‾√

(c) (d) (e) (f) (g) (h) (i)

Question 3: (1 point)

Solve.

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

Question 4: (1 point)

Solve.

−2 − 2 i 3‾√ −2 i 2 1 − i 3‾√ −2 4 −1 + i 3‾√

+ 243 = 0v5

3 3 (cos ( ) + i sin ( ))π5 π5 3 (cos ( ) + i sin ( ))9 π5 9 π5 3 (cos ( ) + i sin ( ))4 π5 4 π5 3 (cos ( ) + i sin ( ))8 π5 8 π5 3 (cos ( ) + i sin ( ))3 π5 3 π5 3 (cos ( ) + i sin ( ))2 π5 2π5 −3 3 (cos ( ) + i sin ( ))7 π5 7 π5

+43 = 52u4

(a) (b) (c) (d)

Question 5: (1 point)

Simplify.

Enter the answer in the standard form of a complex number with the real part in the first answer box and the imaginary part in the second answer box. If the complex number has no real term, enter "0" in the first answer box. If the complex number has no imaginary term, enter "0" in the second answer box.

__________ __________

Question 6: (1 point)

Simplify.

(a) (b) (c) (d)

, i3‾√ 3‾√ ± , ±i3‾√ 3‾√ ±i 3‾√ ± 3‾√

(5 (cos + i sin ))2π3 2π3 4

+ i

(3 + 3i)3

27 (−1 + i)2‾√ −162 + 162 i −54 + 54 i −54 − 54 i

Question 7: (1 point)

Write in trigonometric form.

(a)

(b)

(c)

(d)

(e)

Question 8: (1 point)

Find the quotient .

and

(a)

(b)

(c)

(d)

Question 9: (1 point)

(6 + 6i3‾√ )5

248832 (cos + i sin )7π 6

7π 6

248832 (cos + i sin )5π 6

5π 6

995328 2‾√ (cos + i sin )5π6 5π 6

7962624 (cos + i sin )5π 6

5π 6

7962624 (cos + i sin )7π 6

7π 6

z1 z2

= 12 (cos 210° + i sin 210° )z1 = 2 (cos 90° + i sin 90° )z2

= 24 (cos 120° + i sin 120° ) z1 z2

= 24 (cos 300° + i sin 300° ) z1 z2

= 6 (cos 120° + i sin 120° ) z1 z2

= 6 (cos 300° + i sin 300° ) z1 z2

Find the product .

and

(a)

(b) (c)

(d)

Question 10: (1 point)

Convert the complex number to trigonometric form.

(a) (b) (c) (d)

Question 11: (1 point)

Convert the complex number to trigonometric form.

− +

z1 z2

= 5 (cos 100° + i sin 100° )z1 = 7 (cos 110° + i sin 110° )z2

= (cos 210° + i sin 210°)z1 z2 5 7

= 35 (cos 210° + i sin 210° )z1 z2 = 35 (cos(−10°) + i sin(−10°))z1 z2 = (cos(−10°) + i sin(−10°))z1 z2

5 7

z = 2− 3 i

13‾‾‾√ (cos 56° + i sin 56°) 13‾‾‾√ (cos 304° + i sin 304°) 13‾‾‾√ (cos 304° − i sin 304°)

13 (cos 304° + i sin 304°)

z = 5 5 3‾√ i

(cos + i sin )2π 2π

(a)

(b)

(c)

(d)

Question 12: (1 point)

Determine the modulus of the complex number .

Modulus = __________

Question 13: (1 point)

Plot in the complex plane.

(a)

5 (cos + i sin )2π3 2π3 10 (cos + i sin )π3 π3 10 (cos − i sin )2π3 2π3 10 (cos + i sin )2π3 2π3

z = 96− 28i

z = 5− 3 i

(b)

(c)

(d)