Express the given complex number in the form \(a + ib: i^{-39}\)
Solution and Explanation
\( i^{-39}=i^{-4 × 9-3}\)
\(=(i^{4})^{-9}× i^{-3}\)
\(=\dfrac{1}{i^{-3}}=\dfrac{1}{-i}\)
\(=\dfrac{-1}{i} × \dfrac{i}{i}\)
\(=i\) (Ans.)
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Concepts Used:
Complex Numbers and Quadratic Equations
Complex Number: Any number that is formed as a+ib is called a complex number. For example: 9+3i,7+8i are complex numbers. Here i = -1. With this we can say that i² = 1. So, for every equation which does not have a real solution we can use i = -1.
Quadratic equation: A polynomial that has two roots or is of the degree 2 is called a quadratic equation. The general form of a quadratic equation is y=ax²+bx+c. Here a≠0, b and c are the real numbers.
