Question

Which expression is equivalent to (5-2i)^2-i^3 where i^2=-1?

Answer 1

$\text{use:}\\(a-b)^2=a^2-2ab+b^2\\\\(5-2i)^2=5^2-2\cdot5\cdot2i+(2i)^2=25-20i+2^2i^2\\\\=25-20i+4(-1)=25-20i-4=21-20i\\\\i^3=i^2\cdot i=(-1)i=-i$

$(5-2i)^2-i^3=21-20i-(-i)=21-20i+i=21-19i$