Imaginary Numbers Problem Set 2

Given that \(i=\sqrt{-1}\), which of the following is equivalent to \(i^{71}\)?

\[-(i^{4})-(-i)^{2}\]
In the complex number system, what is the value of the given expression? (Note: \(i=\sqrt{-1}\))

\[\frac{10-2i}{2-3i}\]
If the expression above is rewritten in the form \(a+bi\), where \(a\) and \(b\) are real numbers, what is the value of \(a\) ? (Note: \(i=\sqrt{-1}\))

Which of the following is equivalent to \(\frac{4+7i}{3-2i}\) ? (Note: \(i=\sqrt{-1}\))

\[\frac{3-i^{31}}{6+2i^{43}}\]
If the expression above is rewritten in the form \(a+bi\), where \(a\) and \(b\) are real numbers, what is the value of \(b\) ? (Note: \(i=\sqrt{-1}\))