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

Expert Answers

An illustration of the letter 'A' in a speech bubbles

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`


See eNotes Ad-Free

Start your 48-hour free trial to get access to more than 30,000 additional guides and more than 350,000 Homework Help questions answered by our experts.

Get 48 Hours Free Access
Approved by eNotes Editorial Team