Question

Which of the following is real part of function f(z) = z^2+3z at z=1+i​

Answer 1

Step-by-step explanation:

f(z) = z²+3z

when z = 1+I,

f(z) = (1+i)²+ 3(1+i)

= 1+i²+2i +3+3i

= 1 - 1 +3+5i [ i² =-1]

= 3+5i

real part = 3

imaginary part = 5i

Answer 2

Answer:

Given,

function f(z)= z²+3z.

z=1+i.

To Find,

The real part of the given function f(z)= z²+3z.

Solution,

We can find the real part by substituting the value of z=1+i in the function f(z)= z²+3z.

As we know i is an irrational part. So, every part which doesn't have i is a real part.

After substituting we get= f(z)= (i+1)² + 3 (1+i).

f(z)= i²+1+2i+3+3i= i²+5i+4= -1+5i+4= 5i+3 (i²= -1).

As only 3 doesn't have i. it is the only real part.

Hence, the real part of function f(z)= z²+3z is 3.