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Question 1 of 5: Write each as the product of i and a Real Number
$$\sqrt{-225},\sqrt{-588},\sqrt{-75}$$ $$\sqrt{-225}$$$$\sqrt{-588}$$$$\sqrt{-75}$$ $$\sqrt{-225}$$$$\sqrt{-588}$$$$\sqrt{-75}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Thinking Emoji
A
$$\sqrt{-225}=-15\sqrt{i},\sqrt{-588}=-14\sqrt{3i},\sqrt{-75}=-i\sqrt{3i}$$ $$\sqrt{-225}=-15\sqrt{i}$$$$\sqrt{-588}=-14\sqrt{3i}$$$$\sqrt{-75}=-i\sqrt{3i}$$ $$\sqrt{-225}=-15\sqrt{i}$$$$\sqrt{-588}=-14\sqrt{3i}$$$$\sqrt{-75}=-i\sqrt{3i}$$
B
$$\sqrt{-225}=-15i,\sqrt{-588}=i(-14+\sqrt{3}),\sqrt{-75}=i(-5+\sqrt{3})$$ $$\sqrt{-225}=-15i$$$$\sqrt{-588}=i(-14+\sqrt{3})$$$$\sqrt{-75}=i(-5+\sqrt{3})$$ $$\sqrt{-225}=-15i$$$$\sqrt{-588}=$$$$i(-14+\sqrt{3})$$$$\sqrt{-75}=$$$$i(-5+\sqrt{3})$$
C
$$\sqrt{-225}=15i,\sqrt{-588}=14i\sqrt{3},\sqrt{-75}=5i\sqrt{3}$$ $$\sqrt{-225}=15i$$$$\sqrt{-588}=14i\sqrt{3}$$$$\sqrt{-75}=5i\sqrt{3}$$ $$\sqrt{-225}=15i$$$$\sqrt{-588}=14i\sqrt{3}$$$$\sqrt{-75}=5i\sqrt{3}$$
D
$$\sqrt{-225}=-15i^2,\sqrt{-588}=-14i^2\sqrt{3},\sqrt{-75}=-5i^2\sqrt{3}$$ $$\sqrt{-225}=-15i^2$$$$\sqrt{-588}=-14i^2\sqrt{3}$$$$\sqrt{-75}=-5i^2\sqrt{3}$$ $$\sqrt{-225}=-15i^2$$$$\sqrt{-588}=-14i^2\sqrt{3}$$$$\sqrt{-75}=-5i^2\sqrt{3}$$
E
$$\sqrt{-225}=15-i,\sqrt{-588}=14\sqrt{3}-i,\sqrt{-75}=5\sqrt{3}-i$$ $$\sqrt{-225}=15-i$$$$\sqrt{-588}=14\sqrt{3}-i$$$$\sqrt{-75}=5\sqrt{3}-i$$ $$\sqrt{-225}=15-i$$$$\sqrt{-588}=14\sqrt{3}-i$$$$\sqrt{-75}=5\sqrt{3}-i$$
Question 2 of 5: Simplify
$$(6+4i)-(9+7i)+(-4-8i)$$ $$(6+4i)-(9+7i)+(-4-8i)$$ $$(6+4i)-(9+7i)$$$$+\hspace{.25em}(-4-8i)$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Thinking Emoji
A
$$9+i$$
B
$$-4-2i$$
C
$$-1+14i$$
D
$$-5i+2i^2$$
E
$$-7-11i$$
Question 3 of 5: Simplify
$$(8+2i)(-5+6i)(2+3i)$$ $$(8+2i)(-5+6i)(2+3i)$$ $$(8+2i)(-5+6i)\hspace{.25em}\cdot $$$$(2+3i)$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Thinking Emoji
A
$$-15-25i$$
B
$$-1+80i$$
C
$$-218-80i$$
D
$$-225+105i$$
E
$$-20-105i$$
Question 4 of 5: Simplify
$$\frac{-4+6i}{-5-5i}$$
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Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Thinking Emoji
A
$$-\frac{2}{5}-3i$$
B
$$-\frac{16}{41}+\frac{20}{41}i$$
C
$$-\frac{1}{5}-\frac{2}{5}i$$
D
$$\frac{2i}{5}-\frac{i^2}{5}$$
E
$$-\frac{1}{5}-i$$
Question 5 of 5: Simplify
$$i^{63},i^{48},i^{-101}$$ $$i^{63},i^{48},i^{-101}$$ $$i^{63}$$$$i^{48}$$$$i^{-101}$$
Finish »
Select the Correct Answer Below: Correct! Cool Emoji Not Correct! Thinking Emoji
A
$$i^{63}=i^2,i^{48}=-1,i^{-101}=i$$ $$i^{63}=i^2$$$$i^{48}=-1$$$$i^{-101}=i$$ $$i^{63}=i^2$$$$i^{48}=-1$$$$i^{-101}=i$$
B
$$i^{63}=i,i^{48}=1,i^{-101}=1$$ $$i^{63}=i$$$$i^{48}=1$$$$i^{-101}=1$$ $$i^{63}=i$$$$i^{48}=1$$$$i^{-101}=1$$
C
$$i^{63}=1,i^{48}=i,i^{-101}=-1$$ $$i^{63}=1$$$$i^{48}=i$$$$i^{-101}=-1$$ $$i^{63}=1$$$$i^{48}=i$$$$i^{-101}=-1$$
D
$$i^{63}=-i,i^{48}=1,i^{-101}=-i$$ $$i^{63}=-i$$$$i^{48}=1$$$$i^{-101}=-i$$ $$i^{63}=-i$$$$i^{48}=1$$$$i^{-101}=-i$$
E
$$i^{63}=i,i^{48}=-i,i^{-101}=i$$ $$i^{63}=i$$$$i^{48}=-i$$$$i^{-101}=i$$ $$i^{63}=i$$$$i^{48}=-i$$$$i^{-101}=i$$

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