Question

3. Find the values of a and b such that (a + ib)

2 = i. Hence, or otherwise, solve the

equation z

2 + 2z + 1 − i = 0, leaving your answers in the form a + bi, a, b ∈ R.​

Answer 1

Step-by-step explanation:

Let Z = a + bi

2+2(a+bi) +1-i=0

(3+2a) + (b-1) i = 0

Comparing

Real part = 3 +2a = 0

So a = - 3/2

Imaginary part = b-1=0

b=1

So z = a +b i = - 3/2 + 1 i