SOLUTION: Please help me to solve question value of x and y when (x+yi)^2=5+4i

Algebra ->  Complex Numbers Imaginary Numbers Solvers and Lesson -> SOLUTION: Please help me to solve question value of x and y when (x+yi)^2=5+4i       Log On


   

Question 1150857: Please help me to solve question value of x and y when (x+yi)^2=5+4i
Found 2 solutions by josgarithmetic, math_helper:
Answer by josgarithmetic(39618) About Me  (Show Source):
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
An easy way to solve this is to use polar form of the complex number:
5+4i = +%28sqrt%284%5E2%2B5%5E2%29%29e%5E%28i%2Atheta%29+

where +theta+=+tan%5E-1%284%2F5%29+ = 0.67474 radians to 5 decimal places

5+4i = +6.40312e%5E%28i%2A0.67474%29+

From here, take the square root of the leading coeffiient and divide theta by two:


sqrt%285%2B4i%29+=+2.53044%2Ae%5E%28i%2A0.33737%29+

Using +r%2Ae%5E%28i%2Atheta%29+=+r%2Acos%28theta%29+%2B+r%2Ai%2Asin%28theta%29+:

sqrt%285%2B4i%29+=+2.38780+%2B+i%2A0.83759+

which gives you x and y by direct comparison.

And of course, the negative of that answer, because (-a)^2 = (a)^2