Help pls

z = 24 -32i

Thus, 

|z| = \({\sqrt{24^2 + 32^2}}\)

     = \({\sqrt{1600}}\)

     = 40

Turns out, the previous answer I posted was wrong.

Here's the correct solution :- 

z² = 24 - 32i

Let z = x + iy

⇒ z² = x² + i²y² + 2xiy

         = x² - y² + 2xiy

Now, the real part,

x² - y² = 24                            ...(1)

Imaginary part, 

2xy = -32

xy   = -16

x     = -16/y

From (1)

x² - 256/x² = 24

x⁴ - 256 = 24x²

x⁴ - 24x² - 256 = 0 

Solving this equation, 

x² = -8, 36

⇒x = 6 

   y = -8/3

Thus z = 6 - 8i/3 

         |z| = \({ \sqrt{6^2 + (8/3)^2}}\)

              = 6.57

Hope this helps :)