Square root of a complex number.Date: 6/6/96 at 12:32:47 From: Anonymous Subject: The square root of a complex number. My question is: Find the square root of 5+12i. Hint: Let the square root of 5+12i=a+bi. This is how the question is in my math textbook. I have been trying it for a while now, but have been unable to get the answer. I have tried changing it to polar form and trying to get an answer from that, but it does not seem to lead anywhere. Any help you could give will be greatly appreciated. Thanks, Lindsey Date: 6/14/96 at 1:2:55 From: Doctor Beth Subject: Re: The square root of a complex number. If the square root of a+bi is 5+12i, then you know that (a+bi)^2 = 5+12i. This leads to the equation a^2 + 2abi - b^2 = 5+12i. Whenever two complex numbers are equal, their real parts and imaginary parts are equal, so you have the 2 equations a^2 - b^2 = 5 and 2ab = 12. Since this is two equations with two unknowns, you can probably take it from here. (I did the problem and ended up with something that factored very nicely.) -Doctor Beth, The Math Forum Check out our web site! http://mathforum.org/dr.math/ |
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