Question

Express this complex number in the form of a + ib

i^-39 ( i to the power of negative 39 )
${i }^{ - 39}$​

Answer 1

Answer:

the representation is 0+1i

Step-by-step explanation:

1/i^39=1/(1×-1×i)

=-1/i

=i²/i=i

Answer 2

$\green {\underline { \underline \bold {Answer : - }}}$

• $\iota$

$\red{ \bf \underline{ \underline {Step-by-step \: explanation:-}} }$

$\\ \: \: \: \: \: \: \: \: \: \tt = \dfrac{1}{ { \iota}^{39} } = \frac{1}{ { { (\iota}^{2} )}^{9} \times { \iota}^{3} }$

$\\ \: \: \: \: \: \: \: \: \: \tt = \frac{1}{ {(1)}^{9} \times { \iota}^{3} } = \frac{1}{ { \iota}^{3} } = \frac{1}{ - \iota}$

$\\ \: \: \: \: \: \: \: \: \: \tt = \frac{1}{ - \iota} \times \frac{ \iota}{ \iota} = \frac{ \iota}{ - { \iota}^{2} }$

$\\ \: \: \: \: \: \: \: \: \: \tt = \frac{ \iota}{ - ( - 1)} = \frac{ \iota}{1} = \iota$