Question

Write the expression 2i^15-i^7 in the standard form a + bi

Answer 1

$\bf 2i^{15}-i^7\qquad \begin{cases} i^2=\sqrt{-1}\cdot \sqrt{-1}\implies \sqrt{(-1)^2}\implies -1\\\\ i^4=i^2\cdot i^2\implies -1\cdot -1\implies 1 \end{cases}\\\\ -----------------------------\\\\ 2i^{4+4+4+2+1}-i^{4+2+1}\implies 2i^4i^4i^4i^2i^1-i^4i^2i^1 \\\\\\ (2\cdot 1\cdot 1\cdot 1\cdot -1\cdot i)-(1\cdot -1\cdot i)\implies -2i-(-i) \\\\\\ -2i+i\implies -i\implies \boxed{0-i}$