1.

Simplify : `(i)" "(-2i)((1)/(6)i)" "(ii)" "(-i)(3i)((-1)/(6)i)^(3)" "(iii)" "4 sqrt(-4)+5 sqrt(-9)-3 sqrt(-16)`

Answer» We have
`(i)" "(-2i)((1)/(6)i)+(-2xx(1)/(6))xxi^(2)=(-1)/(3)xx(-1)=(1)/(3)`.
`(ii)" "(-i)(3i)((-1)/(6)i)^(3)=(-3i^(2))((-1)/(216)i^(3))`
`=(-3)xx(-1)[(-1)/(216)xx(-i)]" "[because i^(3) = -i]`
`=(3xx(1)/(216)xxi)=(1)/(72)i`.
`(iii)" "4 sqrt(-4)+5 sqrt(-9)-3 sqrt(-16)`
`=(4xx2i)+(5xx3i)-(3xx4i)" "[because sqrt(-4)=2i, sqrt(-9)=3i, sqrt(-16) = 4i]`
`=(8i + 15i - 12i)=(11)i`.


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