Question

$(-1 + 2i) + \left(\frac{1}{2} - i\right) =$

• A. $\frac{3}{2} + i$
• B. $-\frac{1}{2} - i$
• C. $-\frac{1}{2} + i$
• D. $\frac{1}{2} \pm i$

Hint:

Treat '$i$' just like a variable (like '$x$') during addition and subtraction. Only when performing multiplication do you need to apply the property $i^2 = -1$.

Answer 1

The Correct Option is C

Addition of complex numbers involves grouping the real parts together and the imaginary parts together. Step 1: Group the Real Parts The real parts are $-1$ and $\frac{1}{2}$: $$\text{Real Part} = -1 + \frac{1}{2}$$ $$\text{Real Part} = -\frac{2}{2} + \frac{1}{2} = -\frac{1}{2}$$

Step 2: Group the Imaginary Parts The imaginary parts are $2i$ and $-i$: $$\text{Imaginary Part} = 2i - i$$ $$\text{Imaginary Part} = (2 - 1)i = 1i = i$$

Step 3: Combine Results Combining the simplified parts into the standard form $a + bi$: $$\text{Result} = -\frac{1}{2} + i$$