Simplify-i -2 i 1-6 i ii - i 3 i -1-6 i 3iii 4 -4-5 -9-3 -16

We have (i)( 2i) ( 1/6 i )= ( 2 ×1/6 ) × i^2 = 1/3× ( 1) = 1/3 (ii) ( i)(3i) ( 1/6i )^3 =( 3 i^2) ( 1/216i^3 ) = ( 3) × ( 1) [ 1/216× ( i) ] [∵ i^3= ...

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Byju's Answer

Standard VII

Mathematics

Powers and Exponents

Simplify:i -2...

Question

Simplify:
(i) $(- 2 i) (\frac{1}{6} i)$
(ii) $(- i) (3 i) {(\frac{- 1}{6} i)}^{3}$
(iii) $4 \sqrt{- 4} + 5 \sqrt{- 9} - 3 \sqrt{- 16}$

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Solution

We have
(i) $(- 2 i) (\frac{1}{6} i) = (- 2 \times \frac{1}{6}) \times i^{2} = \frac{- 1}{3} \times (- 1) = \frac{1}{3}$
(ii) $(- i) (3 i) {(\frac{- 1}{6} i)}^{3} = (- 3 i^{2}) (\frac{- 1}{216} i^{3})$

$= (- 3) \times (- 1) [\frac{- 1}{216} \times (- i)]$ $[∵ i^{3} = - i]$

$= (3 \times \frac{1}{216} \times i) = \frac{1}{72} i$

(iii) $4 \sqrt{- 4} + 5 \sqrt{- 9} - 3 \sqrt{- 16}$

$= (4 \times 2 i) + (5 \times 3 i) - (3 \times 4 i)$ $[∵ \sqrt{- 4} = 2 i, \sqrt{9} = 3 i, \sqrt{- 16} = 4 i]$

$= (8 i + 15 i - 12 i) = (11) i$ .

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\frac{11}{12} \div (\frac{5}{9} \times \frac{18}{25})

(ii)

(2 \frac{1}{2} \times \frac{8}{10}) \div (1 \frac{1}{2} + \frac{5}{8})

(iii)

\frac{15}{16}

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(iv)

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(\frac{3}{4} + \frac{3}{5})

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Q. Simplify:

(i)(−8) × 9 + (−8) × 7
(ii) 9 × (−13) + 9 × (−7)
(iii) 20 × (−16) + 20 × 14
(iv) (−16) × (−15) + (−16) × (−5)
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Use the distributivity of multiplication of rational numbers over their addition to simplify:

(i) $\frac{3}{5} \times (\frac{35}{24} + \frac{10}{1})$

(ii) $\frac{- 5}{4} \times (\frac{8}{5} + \frac{16}{5})$

(iii) $\frac{2}{7} \times (\frac{7}{16} - \frac{21}{4})$

(iv) $\frac{3}{4} \times (\frac{8}{9} - 40)$

Q. Simplify:
(i)

{(4^{- 1} \times 3^{- 1})}^{2}

(ii)

{(5^{- 1} \div 6^{- 1})}^{3}

(iii)

{(2^{- 1} + 3^{- 1})}^{- 1}

(iv)

{(3^{- 1} \times 4^{- 1})}^{- 1} \times 5^{- 1}

Q. Simplify:
(i)

{\{4^{- 1} \times 3^{- 1}\}}^{2}

(ii)

{\{5^{- 1} \div 6^{- 1}\}}^{3}

(iii)

{(2^{- 1} + 3^{- 1})}^{- 1}

(iv)

{\{3^{- 1} \times 4^{- 1}\}}^{- 1} \times 5^{- 1}

(v)

(4^{- 1} - 5^{- 1}) \div 3^{- 1}

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Simplify: (i)(−2i)(16i) (ii) (−i)(3i)(−16i)3 (iii) 4√−4+5√−9−3√−16

We have (i)(−2i)(16i)=(−2×16)×i2=−13×(−1)=13 (ii) (−i)(3i)(−16i)3=(−3i2)(−1216i3) =(−3)×(−1)[−1216×(−i)] [∵i3=−i] =(3×1216×i)=172i (iii) 4√−4+5√−9−3√−16 =(4×2i)+(5×3i)−(3×4i) [∵√−4=2i, √9=3i, √−16=4i] =(8i+15i−12i)=(11)i.

Simplify:
(i) $(- 2 i) (\frac{1}{6} i)$
(ii) $(- i) (3 i) {(\frac{- 1}{6} i)}^{3}$
(iii) $4 \sqrt{- 4} + 5 \sqrt{- 9} - 3 \sqrt{- 16}$