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svp [43]
3 years ago
15

Simplify the following expression using imaginary numbers. Express your answer in a + bi form

Mathematics
1 answer:
mamaluj [8]3 years ago
5 0
<h2>Answer:</h2>

0 - 17i

<h2>Step-by-step explanation:</h2>

Given expression;

i⁸⁰ + i³⁸ - i17

To express the expression in the form a+bi;

<em>i. Rewrite the expression such that it contains terms in i²</em>

(i²)⁴⁰ + (i²)¹⁹ - i17

<em>ii. Solve the result from (i) above using the identity i² = -1</em>

We know that the square root of -1 is i. i.e

\sqrt{-1} = i

<em>Squaring both sides gives</em>

<em>=> </em>(\sqrt{-1} )^{2} = i^{2}<em />

=> -1 = i²

Therefore,

i² = -1

<em>Substitute i² = -1 in step (i) above</em>

(-1)⁴⁰ + (-1)¹⁹ - i17

<em>(iii) Solve the result in (ii)</em>

We know that the when a negative number is raised to the power of an even number, the result is a positive number. If it is raised to the power of an odd number, the result is a negative number. Therefore,

(-1)⁴⁰ + (-1)¹⁹ - i17 becomes

1 + (-1) - i17

0 - i17

<em>(iv) Write the result from (iii) in the form a+bi</em>

0 - 17i

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