Question

z square + Z + 1 upon 4​

Answer 1

(z² + z + 1)/4 _____(i)

Take z = a + ib

Then, z² = (a + ib)² = a² + i²b² + 2iab
= a² - b² + 2iab

Now, (i) :

→ [(a² - b² + 2iab) + (a + ib) + 1]/4

= (a²-b²+a+1)/4 + i(2ab+b)/4
→{Real part of z} + {Imaginary part of z}