Question

Evalute (4 + 2i) − (1 − 7i)

Answer 1

Subtacting Complex Numbers

`\boxed{\begin{gathered}\textsf{(a + bi) - (c + di)}\\\\\text{Distribute the minus and}\\\text{combine like terms}\end{gathered}}`

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Question :

Evaluate (4 + 2i) − (1 − 7i)

Calculating :

(4 + 2i) - (1 - 7i)

4 + 2i - 1 + 7i

4 - 1 + 2i + 7i

3 + 9i {answer} we're done!

`\heartsuit`

Answer 2

3 + 9i

Explanation:

In order to evaluate the expression (4 + 2i) - (1 - 7i), distribute the negative sign through the parentheses and then combine like terms:

`\sf (4 + 2i) - (1 - 7i) = 4 + 2i - 1 + 7i`

Now, combine the real parts (numbers without the "i" term) and the imaginary parts (numbers with the "i" term):

`\sf \textsf{ Real parts: }4 - 1 = 3`

`\sf \textsf{ Imaginary parts: } 2i + 7i = 9i`

So, the result is 3 + 9i.