Question

find squens root of 1+4√3i​

Answer 1

Answer:I think that u will be able to understand somthing by this

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Step-by-step explanation:How can we find square root of the complex number

1−43–√i−−−−−−−√?

Now here if I assume square root to be a+ib i.e. a+ib=1−43–√i−−−−−−−√−−−−−−−−−√, then after squaring both sides, how to compare real and imaginary part?

1−43–√i−−−−−−−√=4−3−43–√i−−−−−−−−−−−√=22+3i2−43–√i−−−−−−−−−−−−−√=(2−3–√i)2−−−−−−−−−√ which made calculation easier.

Answer 2

$= \sqrt{1 + 4 \sqrt{3} } \\ \\ = 1 + 2$