Polar system Quiz 1

Question 1

Which of the following is true for the equation $${{i}^{x}} > {{i}^{y}}$$?

Accepted Answer

$$x$$ is $$4$$ multiple and $$y$$ $$2$$

Answer

$$x$$ is $$4$$ multiple and $$y$$ is $$2$$ multiple

Answer

$$x$$ is $$4$$ multiple and $$y$$ is $$3$$ multiple

Answer

$$x$$ is $$4$$ multiple and $$y$$ is $$5$$ multiple

Question 2

Show $$\sqrt{7}i$$ using polar coordinates?

Accepted Answer

$$z=\sqrt{7}\left( \cos \left( \dfrac{\pi }{2} \right)+i\sin \left( \dfrac{\pi }{2} \right) \right)$$

Answer

$$z=\sqrt{7}\left( \cos \left( \dfrac{\pi }{2} \right)-i\sin \left( \dfrac{\pi }{2} \right) \right)$$

Answer

$$z=7\left( \cos \left( \dfrac{\pi }{2} \right)+i\sin \left( \dfrac{\pi }{2} \right) \right)$$

Answer

$$z=49\left( \cos \left( \dfrac{\pi }{2} \right)+i\sin \left( \dfrac{\pi }{2} \right) \right)$$

Question 3

If $$r=a$$ and $$	ext{ }\!\!	heta\!\!	ext{ }={{	an }^{-1}}\left( \dfrac{b}{c} ight)$$ for the point $$\left( \sqrt{10},3 ight)$$ then find $${{a}^{2}}+{{b}^{2}}+{{c}^{2}}$$?

Accepted Answer

$$38$$

Answer

$$19$$

Answer

$$31$$

Answer

$$25$$

Question 4

If the rectangular point for a polar coordinate $$\left( 2,\dfrac{	ext{ }\!\!\pi\!\!	ext{ }}{4} ight)$$ is $$\left( a,b ight)$$ then find $$ab$$

Accepted Answer

$$2$$

Answer

$$\sqrt{3}$$

Answer

$$\sqrt{5}$$

Answer

$$\sqrt{2}$$

Question 5

Convert the given equation into an equation in terms of polar coordinates. $$ \ \dfrac{339{{x}^{2}}}{113{{x}^{2}}+113{{y}^{2}}}=226-xy$$.

Accepted Answer

$$3{{\cos }^{2}}	heta =226-{{r}^{2}}\cos 	heta \sin 	heta $$

Answer

$$3{{\cos }^{2}}	heta {{\sin }^{2}}	heta =226-{{r}^{2}}\cos 	heta \sin 	heta $$

Answer

$$3\cos 	heta \sin 	heta =226-{{r}^{2}}\cos 	heta \sin 	heta $$

Answer

$$3{{\sin }^{2}}	heta =226-{{r}^{2}}\cos 	heta \sin 	heta $$