Math  /  Algebra

QuestionSimplify. 7+(818i)-7+(8-18 i)
Write your answer in the form a+bi\mathrm{a}+\mathrm{bi}. \square ii

Studdy Solution

STEP 1

What is this asking? We're taking a complex number 818i8 - 18i and adding 7-7 to it.
We need to simplify the expression and write the answer in the standard form a+bia + bi. Watch out! Don't forget that the real and imaginary parts are like apples and oranges – they can't be combined directly!

STEP 2

1. Group the real and imaginary parts.
2. Simplify the expression.

STEP 3

First, let's **identify** the real and imaginary parts of our complex number.
We have 7-7 as our **real part** and (818i)(8 - 18i) as another complex number with a **real part** of 88 and an **imaginary part** of 18i-18i.

STEP 4

We can **regroup** the expression to put the real parts together.
Remember, we're adding 7-7 to the entire complex number (818i)(8 - 18i), so we can rewrite our expression as: 7+(818i)=7+818i-7 + (8 - 18i) = -7 + 8 - 18i

STEP 5

Now, let's **combine** those real numbers!
We have 7+8-7 + 8.
We can think of this as adding 88 to 7-7.
Since 88 is larger than 77, the result will be positive.
The difference between 88 and 77 is 11, so 7+8=1-7 + 8 = 1.

STEP 6

So, our simplified expression becomes: 118i1 - 18i

STEP 7

Our simplified complex number is 118i1 - 18i, which is in the beautiful standard form of a+bia + bi, where a=1a = 1 and b=18b = -18.

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