Let's start by simplifying the given equation iz2+z−z+i=0. Notice that the terms z−z cancel each other out: iz2+i=0 Next, factor out the common factor i from the equation: i(z2+1)=0 For this product to be zero, either i=0 or z2+1=0. Since i is the imaginary unit √−1 and cannot be zero, we are left with: z2+1=0 Subtract 1 from both sides: z2=−1 Taking the square root of both sides, we get: z=±i Now we need to find the value of (|z|+1)2. The magnitude (or modulus) of z is calculated as follows: |z|=|i|=1 Therefore, we have: |z|+1=1+1=2 Finally, we square this result: (|z|+1)2=22=4