Question

express i-39 (iota raised to the power minus 39) in the form of a+ib

Answer 1

that's the required answer

Answer 2

$\displaystyle \sf{ {i}^{ - 39} = 0 + 1.i }$

Which is of the form a + ib Where a = 0 , b = 1

Given :

The expression $\displaystyle \sf{ {i}^{ - 39} }$

To find :

To express in the form a + ib

Solution :

Step 1 of 2 :

Write down the given expression

The given expression is

$\displaystyle \sf{ {i}^{ - 39} }$

Step 2 of 2 :

Express in the form a + ib

We know " i " is the complex number satisfying the property i² = - 1

$\displaystyle \sf{ {i}^{ - 39} }$

$\displaystyle \sf{ = \frac{1}{ {i}^{39} } }$

$\displaystyle \sf{ = \frac{i}{ {i}^{39} \times i} }$

$\displaystyle \sf{ = \frac{i}{ {i}^{39 + 1} } }$

$\displaystyle \sf{ = \frac{i}{ {i}^{40} } }$

$\displaystyle \sf{ = \frac{i}{ ({i)}^{2 \times 20} } }$

$\displaystyle \sf{ = \frac{i}{ ({ {i}^{2} )}^{ 20} } }$

$\displaystyle \sf{ = \frac{i}{ {( - 1)}^{ 20} } }$

$\displaystyle \sf{ = \frac{i}{ 1} }$

$\displaystyle \sf{ = i }$

$\displaystyle \sf{ = 0 + 1.i }$

Which is of the form a + ib

Where a = 0 , b = 1

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