Question

$\sqrt{i}$

❖ᴏɴʟʏ ᴘʀᴏᴘᴇʀ ꜱᴏʟᴠᴇᴅ ᴀɴꜱᴡᴇʀ ᴡɪᴛʜ ɢᴏᴏᴅ ᴇxᴘʟᴀɴᴀɪᴏɴ ɴᴇᴇᴅᴇᴅ
❖ ɴᴏ ꜱᴘᴀᴍᴍɪɴɢ
❖ᴏɴʟʏ ꜰᴏʀ ᴍᴏᴅᴇʀᴀᴛᴏʀꜱ, ʙʀᴀɪɴʟʏ ꜱᴛᴀʀꜱ ᴀɴᴅ ᴏᴛʜᴇʀ ʙᴇꜱᴛ ᴜꜱᴇʀꜱ​​​​​

Answer 1

$\sqrt{i} = a + ib \\ i = (a + ib {)}^{2} \\ i = {a}^{2} + {i}^{2} {b}^{2} + 2abi \\ i = {a}^{2} - {b}^{2} + 2abi \\ \sqrt{i} = \underline{ + } \bigg( \frac{1}{ \sqrt{2} } + i \: \frac{ \sqrt{2} }{2} \bigg) \\ \sqrt{i} = \underline{ +} \bigg( \frac{ \sqrt{2} }{2} + i \: \frac{ \sqrt{2} }{2} \bigg)$

Answer 2

Answer:

$\huge \mathcal \blue{Answer}$

$\sqrt{i} = a + ib \\ i = (a + ib {)}^{2} \\ i = {a}^{2} + {i}^{2} {b}^{2} + 2abi \\ i = {a}^{2} - {b}^{2} + 2abi \\ \sqrt{i} = \underline{ + } \bigg( \frac{1}{ \sqrt{2} } + i \: \frac{ \sqrt{2} }{2} \bigg) \\ \sqrt{i} = \underline{ +} \bigg( \frac{ \sqrt{2} }{2} + i \: \frac{ \sqrt{2} }{2} \bigg)$

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