(iii)z =−2/(1 + √3i)

To solve for z in the equation z = -2/(1 + √3i), we can follow these steps:

Step 1: Write the denominator in a+bi form The denominator is already in this form (a+bi), where a=1 and b=√3.

Step 2: Multiply the numerator and the denominator by the conjugate of the denominator The conjugate of 1 + √3i is 1 - √3i. So, we multiply both the numerator and the denominator by this conjugate:

-2(1 - √3i) / (1 + √3i)(1 - √3i)

Step 3: Simplify the expression The numerator simplifies to -2 + 2√3i.

The denominator simplifies to 1 - (√3i)^2 = 1 - 3 = -2.

So, the expression simplifies to (-2 + 2√3i) / -2.

Step 4: Divide the real and imaginary parts by -2 This gives us z = 1 - √3i.