Question

simplify each expression. choose the correct answer from each drop - down menu.
a) ((2 - 5i)+(3 + 7i)=square)
b) ((-6 + i)-(1 - 4i)=square)

Explanation:

Part (a)

Step1: Combine real parts

Real parts: \(2\) and \(5\). Sum: \(2 + 5=7\)

Step2: Combine imaginary parts

Imaginary parts: \(-5i\) and \(7i\). Sum: \(-5i + 7i = 2i\)

Step3: Combine results

Add real and imaginary parts: \(7 + 2i\)

Step1: Distribute the subtraction

\((-6 + i)-(1 - 4i)=-6 + i - 1 + 4i\)

Step2: Combine real parts

Real parts: \(-6\) and \(-1\). Sum: \(-6-1=-7\)

Step3: Combine imaginary parts

Imaginary parts: \(i\) and \(4i\). Sum: \(i + 4i = 5i\)

Step4: Combine results

Add real and imaginary parts: \(-7 + 5i\)

Answer:

\(7 + 2i\)

Part (b)