Question

Write the complex number in polar form with argument theta between 0 and 2 pie

Answer 1

`=\text{ 7}\sqrt[]{2}\lbrack cos(tan^(-1)(-1)\text{ + isin}(tan^(-1)(-1)\text{ \rbrack}`Step-by-step explanation:
`\begin{gathered} let\text{ z = -7 + 7i} \\ r\text{ = }\sqrt[]{(-7)^2+(7)^2} \\ r\text{ = }\sqrt[]{49+49\text{ }}\text{ = }\sqrt[]{98} \\ r\text{ = 7}\sqrt[]{2} \end{gathered}`
`\begin{gathered} \tan \text{ }\theta\text{ = }(7)/(-7)\text{ = -1} \\ \text{ }\theta=tan^(-1)(-1) \\ \end{gathered}`
`\begin{gathered} z\text{= }r(\cos \theta+\text{ isin}\theta) \\ -7\text{ + 7i }=\text{ }r(\cos \theta+\text{ isin}\theta) \\ =\text{ 7}\sqrt[]{2}\lbrack cos(tan^(-1)(-1)\text{ + isin}(tan^(-1)(-1)\text{ \rbrack} \end{gathered}`

The answer in polar form:

`=\text{ 7}\sqrt[]{2}\lbrack cos(tan^(-1)(-1)\text{ + isin}(tan^(-1)(-1)\text{ \rbrack}`