91Ó°ÊÓ

The problems that follow review material we covered in Section 4.6. Graph each equation. $$ y=x+\cos \pi x, 0 \leq x \leq 8 $$

Find the following products. \(4 i(1-i)^{2}\)

Show that \(x=1 / 2+(\sqrt{3} / 2) i\) is a cube root of \(-1\).

Find the following quotients. Write all answers in standard form for complex numbers. \(\frac{2 i}{3+i}\)

The problems that follow review material we covered in Section 4.6. Graph each equation. $$ y=3 \sin x+\cos 2 x, 0 \leq x \leq 4 \pi $$

De Moivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of \(x\) is \(1 / x\), which can be expressed as \(x^{-1}\). Use this fact, along with de Moivre's Theorem, to find the reciprocal of each number below. $$ 1+i $$

Find the following quotients. Write all answers in standard form for complex numbers. \(\frac{3 i}{2+i}\)

The problems that follow review material we covered in Section 4.6. Graph each equation. $$ y=\sin x+\frac{1}{2} \cos 2 x, 0 \leq x \leq 4 \pi $$

Find the following quotients. Write all answers in standard form for complex numbers. \(\frac{2+3 i}{2-3 i}\)

De Moivre's Theorem can be used to find reciprocals of complex numbers. Recall from algebra that the reciprocal of \(x\) is \(1 / x\), which can be expressed as \(x^{-1}\). Use this fact, along with de Moivre's Theorem, to find the reciprocal of each number below. $$ \sqrt{3}-i $$