what is the square root of the complex number 7-24i?

1 Answer

embizze's profile pic

embizze | High School Teacher | (Level 2) Educator Emeritus

Posted on

Find the square root of `7-24i` :



The real parts are equal, as are the real coefficients of the imaginary parts:



`ab=-12==>a=-12/b` Substituting we get:





Since b is real b=3 or -3

`a^2-9=7 ==> a^2=16 ==> a=+-4`

Since ab=-12 one of a or b is negative.

So either of `z=4-3i` or `z=-4+3i` is a square root of `7-24i`