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nikitadnepr [17]
3 years ago
12

Tìm căn bậc hai của số phức z=1+i√3

Mathematics
1 answer:
Anni [7]3 years ago
5 0

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>

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