0 - 17i
Given expression;
i⁸⁰ + i³⁸ - i17
To express the expression in the form a+bi;
i. Rewrite the expression such that it contains terms in i²
(i²)⁴⁰ + (i²)¹⁹ - i17
ii. Solve the result from (i) above using the identity i² = -1
We know that the square root of -1 is i. i.e
[tex]\sqrt{-1} = i[/tex]
Squaring both sides gives
=> [tex](\sqrt{-1} )^{2} = i^{2}[/tex]
=> -1 = i²
Therefore,
i² = -1
Substitute i² = -1 in step (i) above
(-1)⁴⁰ + (-1)¹⁹ - i17
(iii) Solve the result in (ii)
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
(iv) Write the result from (iii) in the form a+bi
0 - 17i
