Imaginary Numbers Problem Set 1

\[(12-7i)-(6+3i)\]
In the complex number system, what is the value of the given expression? (Note: \(i=\sqrt{-1}\))

What is the sum of the complex numbers \(3-4i^{2}\) and \(2-8i^{3}\)? (Note: \(i=\sqrt{-1}\))

\[(3-5i)(4-2i)=a+bi\]
In the equation above \(a\) and \(b\) are real numbers and \(i=\sqrt{-1}\) . What is the value of \(a-b\)?

For \(i=\sqrt{-1}\), which of the following is equivalent to \(2i(-3i+4)\)?

What is the integer value of the complex expression \(9i^{8}+4i^{6}-2i^{2}\)?