Math Sat Weekly assessment Jan-10-25

Given that  \(i = \sqrt{-1} \), what is the sum of the complex numbers \( (21i^2 – 12 i) + (3 – 5i)\)?

What is the result of the multiplication \((5 – 6i)(3+3i) ?( Note: i = \sqrt{-1})\)

Which of the following is equivalent to \( \frac{38+18i}{4+6i}\)?\((Note: i=\sqrt{-1})\)

if the expression above is expected in the form \( a + bi\), where \( i  = \sqrt{-1}\), what is the value of b?

if the expression \( \frac{-3i^2 + 2i}{2 + i}\) is written in the form  \( a + bi\), where a and b are real numbers and \( i = \sqrt{-1}\), what  is the value of a ?