Question

what is one of the square roots of 3+ 4i, where i =sqrt{ - 1}





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Answer 1

Answer:

(2+i)

Step-by-step explanation:

Let 3+4i=x+iy

Then (3+4i)2=(x+iy)2⇒3+4i=x−y+2ixy

Comparing real part and imaginary part, we get

3=x−y and 2xy=4⇒xy=4

∴x+y=±5     ( As x=−5;x is real part )

∴x=4,y=1⇒x=±2,y=±1

Hence square root is ±(2+i)

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