- #1
aisha
- 584
- 0
does anyone know how to find the square root of 5+12i ?
Hurkyl said:Try asking yourself the same question written differently:
Can you find a number z such that z*z = 5 + 12i?
Actually... no, that's wrong. The answer is 3 + 2i.aisha said:This was a multiple choice question so the answer is 2+i
phreak said:Actually... no, that's wrong. The answer is 3 + 2i.
aisha said:can u please tell me how you got that answer?
The formula for finding the square root of a complex number is √(a+bi) = ± (c+di), where c and d are the real and imaginary parts of the square root and are calculated using the following equations: c = √((a+√(a^2+b^2))/2) and d = ± (√((√(a^2+b^2)-a)/2)), where a and b are the real and imaginary parts of the complex number.
To simplify a complex number before finding its square root, you need to first determine its modulus or absolute value, which is given by √(a^2+b^2). Then, divide the real and imaginary parts of the complex number by the modulus to get a simplified form of the complex number.
To calculate the square root of 5+12i, you first need to simplify the complex number by dividing both the real and imaginary parts by its modulus, which is √(5^2+12^2) = √(25+144) = √169 = 13. This gives us a simplified form of (5/13)+(12/13)i. Then, using the formula mentioned in the first question, we can calculate the square root as √(5+12i) = ± (√((5/13)+i(12/13))).
The square root of a complex number can be represented on a complex plane as a point or vector that lies on the line connecting the origin (0,0) and the original complex number. The length of this point or vector is equal to the magnitude or modulus of the square root, and its direction is determined by the argument or angle of the original complex number.
To check the accuracy of your calculated square root of a complex number, you can simply square the result and see if it is equal to the original complex number. If it is, then your calculated square root is correct. You can also plot the original complex number and the calculated square root on a complex plane to visually confirm their accuracy.