Imaginary numbers Quiz 1

Question 1

Solve $$\left( {6 - 5i} \right)\left( {8 + 11i} \right)$$

Accepted Answer

$$103 + 16i$$

Answer

$$103 - 16i$$

Answer

$$108 + 6i$$

Answer

$$116 + 16i$$

Question 2

Perform the indicated oppression: $$\dfrac{{8 + 7i}}{{6 - i}}$$

Accepted Answer

$$\dfrac{{41}}{{37}} + \dfrac{{50i}}{{37}}$$

Answer

$$\dfrac{{47}}{{37}} + \dfrac{{53i}}{{37}}$$

Answer

$$\dfrac{{78}}{{37}} - \dfrac{{53i}}{{37}}$$

Answer

$$\dfrac{{36}}{{37}} - \dfrac{{43i}}{{37}}$$

Question 3

Find the modulus of $$\left( {4 - 3i} \right)\left( { - 2 + 7i} \right)$$

Accepted Answer

$$5\sqrt {53} $$

Answer

$$5\sqrt {55} $$

Answer

$$7\sqrt {53} $$

Answer

$$8\sqrt {63} $$

Question 4

Solve to find the modulus and principal amplitude of $$ - 5$$ and write the answer?

Accepted Answer

$$5,\pi $$

Answer

$$7, - \pi $$

Answer

$$5, - \pi $$

Answer

$$6,\dfrac{\pi }{2}$$

Question 5

If the cube roots of unity are $$1,\omega ,{\omega ^2}$$, then find the roots of the equation $$\left( {x - 2} \right) + 64 = 0$$

Accepted Answer

$$ - 2,{	ext{ }}2 - 4\omega ,{	ext{ }}2 - 4{\omega ^2}$$

Answer

$$4,{	ext{ 6}} + 4\omega ,{	ext{ 6}} + 4{\omega ^2}$$

Answer

$$ - 1,{	ext{ 1}} - 4\omega ,{	ext{ 1}} - 4{\omega ^2}$$

Answer

$$2,{	ext{ }}2 + 4\omega ,{	ext{ }}2 + 4{\omega ^2}$$