Question

the value of i^(-35) is
•i
•-i
•1
•-1​

Answer 1

Answer:

$\sf \dashrightarrow \: {i}^{ - 35} \\ \\ \sf \dashrightarrow \: \frac{1}{ {i}^{35} } \\ \\ \sf \dashrightarrow \: \frac{1}{(i {}^{2}) {}^{17} \times i } \\ \\ \sf \bullet \: {i}^{2} = - 1\\ \\ \sf \dashrightarrow \: \frac{1}{( - 1) {}^{17} \times i } \\ \\ \sf \dashrightarrow \: \frac{1}{ - 1 \times i} \\ \\ \sf \: rationalising \: the \: denominator : - \\ \\ \sf \dashrightarrow \: \frac{1}{ - i} \times \frac{i}{i} \\ \\ \sf \dashrightarrow \: \frac{i}{ - {i}^{2} } \\ \\ \sf \dashrightarrow \: \frac{i}{ - ( - 1)} \\ \\ \sf \: = i$

━━━━━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Done࿐

Answer 2

$\Large{\bold{\blue{\underline{\red{A}\pink{ns}\green{we}\purple{r:-}}}}}$

$\rm{\mapsto The \: value \:of \: {i}^{-35} = i}$

$\Large{\bold{\pink{\underline{\green{G}\purple{iv}\orange{en}\red{:-}}}}}$

$\rm{\leadsto {i}^{-35}}$

$\Large{\bold{\blue{\underline{\red{To}\:\pink{Fin}\green{d}\purple{:-}}}}}$

$\rm{\leadsto The \: value \:of \: {i}^{-35} = \: ?}$

$\Large{\bold{\pink{\underline{\red{So}\purple{lut}\green{ion}\orange{:-}}}}}$

$\tt{:\implies {i}^{ - 35} }$

If the exponent is negative, change it a fraction,

$\tt{:\implies \dfrac{1}{ {i}^{35}}}$

i³⁵ is calculated with exponent divided,

$\tt{:\implies \dfrac{1}{ {i}^{4 \times 8 \times 3} } }$

Calculate using i⁴ = 1

$\tt{:\implies \dfrac{1}{( {{1}^{4})}^{8} {i}^{3} } }$

It is i⁴ = 1,

$\tt{:\implies \dfrac{1}{ {1}^{8} {i}^{3} } }$

Calculate power,

$\tt{:\implies \dfrac{1}{1 {i}^{3} } }$

i² is -1 so it is i³ = i² × i¹ = -i,

$\tt{:\implies \dfrac{1}{1 \times ( - i)} }$

Multiply any number by 1 does not change the value,

$\tt{:\implies \dfrac{1}{ - i} }$

Multiply denominator and numerator by i,

$\tt{:\implies \dfrac{1i}{ - ii} }$

It is i × -i = -i × i = -1,

$\tt{:\implies \dfrac{1i}{1} }$

Multiply any number by 1 does not change the value,

$\tt{:\implies \dfrac{i}{1} }$

If the denominator is 1, the denominator can be removed,

$\bf{:\implies \underline{ \: \: \underline{ \red{ \: i \: }} \: \: }}$

Hence, the value of i^-35 is i.