Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Write <em>z</em> in polar form:
<em>z</em> = 1 + √3 <em>i</em> = 2 exp(<em>i</em> <em>π</em>/3)
Taking the square root gives two possible complex numbers,
√<em>z</em> = √2 exp(<em>i</em> (<em>π</em>/3 + 2<em>kπ</em>)/2)
with <em>k</em> = 0 and <em>k</em> = 1, so that
√<em>z</em> = √2 exp(<em>i</em> <em>π</em>/6) = √(3/2) + √(1/2) <em>i</em>
and
√<em>z</em> = √2 exp(<em>i</em> 7<em>π</em>/6) = -√(3/2) - √(1/2) <em>i</em>
