Algebra 2 Recovery - U1

Multiple Choice

Question 1: Power i

simplify it

$$i^{130}$$  = ?

• $$i$$  

• $$-i$$  

• 1

• -1

Multiple Choice

Question 2: Power i

simplify it

$$i^{141}$$  = ?

• $$i$$  

• $$-i$$  

• 1

• -1

Multiple Choice

Question 3: Power i

simplify it

$$i^{152}$$  = ?

• $$i$$  

• $$-i$$  

• 1

• -1

Multiple Choice

Question 4: Power i simplify it

$$i^{163}$$  = ?

• $$i$$  

• $$-i$$  

• 1

• -1

Multiple Choice

Question 5: {4 cases: a = a + 0i, -a = -a + 0i, bi = 0 + bi, -bi = 0 - bi}

Choose the equivalent complex form to rewrite the given following:

$$\pi i$$  

•  = $$\pi$$  - $$0i$$  

•  = $$\pi$$  + $$0i$$  

•  = 0 + $$\pi i$$  

•  = 0 - $$\pi i$$  

Multiple Choice

Question 6: {4 cases: a = a + 0i, -a = -a + 0i, bi = 0 + bi, -bi = 0 - bi}

Choose the equivalent complex form to rewrite the given following:

$$-\pi i$$  

•  = $$\pi$$  - $$0i$$  

•  = $$\pi$$  + $$0i$$  

•  = 0 + $$\pi i$$  

•  = 0 - $$\pi i$$  

Multiple Choice

Question 7: {4 cases: a = a + 0i, -a = -a + 0i, bi = 0 + bi, -bi = 0 - bi}

Choose the equivalent complex form to rewrite the given following:

$$i\sqrt[]{5}$$  

•  = $$\sqrt[]{5}$$   - $$0i$$  

•  = $$\sqrt[]{5}$$   + $$0i$$  

•  = 0 + $$i\sqrt[]{5}$$   

•  = 0 - $$i\sqrt[]{5}$$   

Multiple Choice

Question 8: {4 cases: a = a + 0i, -a = -a + 0i, bi = 0 + bi, -bi = 0 - bi}

Choose the equivalent complex form to rewrite the given following:

$$-\sqrt[]{5}$$  

•  = $$-\sqrt[]{5}$$   - $$0i$$  

•  = $$\sqrt[]{5}$$   + $$0i$$  

•  = 0 + $$i\sqrt[]{5}$$   

•  = 0 - $$i\sqrt[]{5}$$   

Multiple Choice

Question 9: Radical of negative numbers { $$\sqrt[]{-a}\ =\ i\sqrt[]{a}$$ }

$$\sqrt{-50}$$  =

• $$5i\sqrt{2}$$  

• $$i\sqrt{5}$$   

• $$2i\sqrt{5}$$  

• $$25i\sqrt{2}$$  

Multiple Choice

Question 10: Radical of negative numbers { $$\sqrt[]{-a}\ =\ i\sqrt[]{a}$$ }

$$\sqrt{-243}$$  =

• $$3i\sqrt{3}$$  

• $$9i\sqrt{3}$$  

• $$81i\sqrt{3}$$  

• $$3i\sqrt{81}$$  

Multiple Choice

Question 11: Simply the complex operations following:

(7 + 2i) - (-12 - 4i)

• -5 - 2i

• 19 - 2i

• -5 + 6i

• 19 + 6i

Multiple Choice

Question 12: Simply the complex operations following:

(5-2i) + (-7+8i)

• -2+6i

• 12+6i

• -35-16i²

• -35 -16i

Multiple Choice

Question 13: Simply the complex operations following:

  (10+ 15i) - (48 - 30i)

• 58 - 45i

• 58 - 15i

• -38 - 15i

• -38 + 45i

Multiple Choice

Question 14: Simply the complex operations following:

$$\left(-1-6i\right)\ +\ \left(-7-2i\right)$$  

• $$-7-2i$$  

• $$-8-8i$$  

• $$6+4i$$  

• $$6-8i$$  

Multiple Choice

Question 15: {Distributive product and treat i like x}

-4(2 - 3i)

• -8 + 12i

• 8 - 12i

• 20i

• -4i

Multiple Choice

Question 16: {Distributive product and treat i like x}

-2(4 - 5i)

• -8 + 10i

• 8 - 10i

• -18i

• 2i

Multiple Choice

Question 17: {Distributive product and treat i like x}

$$\left(-1-2i\right)\left(-6-6i\right)$$  

• $$-7+16i$$  

• $$24+24i$$  

• $$12+12i$$  

• $$-6+18i$$  

Multiple Choice

Question 18: {Distributive product and treat i like x}

$$\left(4+6i\right)\left(-6+4i\right)$$  

• $$-54-16i$$  

• $$-52i$$  

• $$52i$$  

• $$-48-20i$$  

Multiple Choice

Question 19: {Just change operation of imagine "i" from positive to negative or the other way around}

2 - 3i

• -2 + 3i

• 2 + 3i

• -2 - 3i

• 2 - 3i

Multiple Choice

Question 20: {Just change operation of imagine "i" from positive to negative or the other way around}

6i + 2

• -6i - 2

• -6i + 2

• 6i + 2

• 2 + 6i

Multiple Choice

Question 21: {Multiply with the conjugate of the give denominator for top and bottom for the following expression}

Simplify: $$\frac{-5}{2\ +\ 3i}$$  

• $$\frac{-10-15i}{4-9i}$$  

• $$\frac{-10\ +\ 15i}{13}$$  

• $$\frac{10\ +\ 15i}{4\ +9i}$$  

• $$\frac{10\ +\ 15i}{13}$$  

Multiple Choice

Question 22: {Multiply with the conjugate of the give denominator for top and bottom for the following expression}

Simplify: $$\frac{3+2i}{5\ -3i}$$  

• $$\frac{21\ -i}{34}$$  

• $$\frac{21+i}{34}$$  

• $$\frac{9\ -19i}{34}$$  

• $$\frac{9+19i}{34}$$  

Multiple Choice

Question 23: {Isolate for x, then taking square-root for both sides. Remember x with have two [positive and negative] solutions}

Solve by for x:

2x² = 18

• x = 5 or -5

• x = 3 or -3

• x = 7 or -3

• x = -7 or 3

Multiple Choice

Question 24: {Isolate for x, then taking square-root for both sides. Remember x with have two [positive and negative] solutions}

Solve for x:

x² - 1 = 48

• x=7,12

• x=±7

• x=1,-13

• x=43,-55

Multiple Choice

Question 25:

two roots x = 2 and x = -1 . Determine the matching quadratic equation

(hint you will work backward: (x - 2)(x + 1)

• x² + 3x - 2

• x² - 3x - 2

• x² + x - 2

• x² - x - 2

Multiple Choice

Question 26:

Solve for x by factoring: x² - 13 = 0

• (x - 13)(x + 13)

  then

  x =13 and x = -13

• (x - $$\sqrt[]{13}$$  )(x + $$\sqrt[]{13}$$  

  then

  x = $$\sqrt[]{13}$$  and x = $$-\sqrt[]{13}$$  

• (x - $$i\sqrt[]{13}$$  )(x + $$i\sqrt[]{13}$$  

  then

  x = $$i\sqrt[]{13}$$  and x = $$-i\sqrt[]{13}$$  

• (x - 6)(x - 7)

  then

  x =6 and x = 7

Multiple Choice

Question 27: Solve for x by Factoring

x² - 8x + 15 = 0

• (x + 5) ( x + 3)

  then

  x = -5 and x = -3

• (x - 5) (x - 3)

  then

  x = 5 and x = 3

• (x + 15) (x - 1)

  then

  x = -15 and x = 1

• (x - 5) (x + 3)

  then

  x = 5 and x = -3

Multiple Choice

Question 28:

Solve for k by Factoring

k² + 12k + 35 = 0

• (k + 5)(k + 7)

  Thus,

  k = -5 and k = -7

• (k + 4)(k + 3)

  Thus,

  k = -4, and k = -3

• (k + 7)(k - 5)

  Thus,

  k = -7, and k = 5

• (k + 3)(k + 5)

  Thus,

  k = -3 and k = -5

Multiple Choice

Identify a, b and c in the quadratic equation: $$2x^2-3x-5=0$$  

• a = 2 , b = 3, c = -5

• a = 2, b = -3, c = 5

• a = 2, b = -3, c = -5

• a = -2, b = 3, c = 5

Multiple Choice

Using the calculator to solve it:

15x² + x - 2 = 0

• Two real solution:

  x = -1/3

  x = 2/5

• Two real solution:

  x = 1/3

  x = -2/5

• Two complex solution:

  x = -1/3 + i

  x = 2/5 - i

• Two complex solution:

  x = 1/3 + i

  x = -2/5 - i