Problem

Find the square root of
\[
16 i
\]
that graphs in the first quadrant.
\[
[?]\left(\cos []^{\circ}+i \sin []^{\circ}\right)
\]

Answer

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Hide Steps

Answer

\( z = \pm 4 e^{i(\frac{\pi}{4}+k\pi)} \)

Steps

Step 1 ：\( z = \sqrt{16i} \)

Step 2 ：\( 16i = 16e^{i(\frac{\pi}{2}+2k\pi)} \)

Step 3 ：\( z = \pm 4 e^{i(\frac{\pi}{4}+k\pi)} \)

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