Question

1. express each number in terms of ( i ).

a.) ( sqrt{-36} )
b.) ( \frac{1}{2}sqrt{-64} )
c.) ( sqrt{-72} )
d.) ( sqrt{-3} )
e.) ( -sqrt{-300} )

Explanation:

Step1: Rewrite sqrt(-n) as sqrt(n)i

For part a: $\sqrt{-36} = \sqrt{36} \cdot i$

Step2: Simplify sqrt(36)

$\sqrt{36} = 6$, so $\sqrt{-36} = 6i$

Step1: Rewrite sqrt(-n) as sqrt(n)i

For part b: $\frac{1}{2}\sqrt{-64} = \frac{1}{2} \cdot \sqrt{64} \cdot i$

Step2: Simplify sqrt(64)

$\sqrt{64} = 8$, so $\frac{1}{2} \cdot 8i = 4i$

Step1: Rewrite sqrt(-n) as sqrt(n)i

For part c: $\sqrt{-72} = \sqrt{72} \cdot i$

Step2: Simplify sqrt(72)

$\sqrt{72} = \sqrt{36 \cdot 2} = 6\sqrt{2}$, so $\sqrt{-72} = 6\sqrt{2}i$

Step1: Rewrite sqrt(-n) as sqrt(n)i

For part d: $\sqrt{-3} = \sqrt{3} \cdot i = \sqrt{3}i$

Step1: Rewrite sqrt(-n) as sqrt(n)i

For part e: $-\sqrt{-300} = -\sqrt{300} \cdot i$

Step2: Simplify sqrt(300)

$\sqrt{300} = \sqrt{100 \cdot 3} = 10\sqrt{3}$, so $-\sqrt{-300} = -10\sqrt{3}i$

Answer:

a.) $6i$
b.) $4i$
c.) $6\sqrt{2}i$
d.) $\sqrt{3}i$
e.) $-10\sqrt{3}i$