QuestionCalculate $(9+9 i)(\overline{9+9 i})$ .

Studdy Solution

STEP 1

Assumptions1. We are given a complex number $9+9i$ and its conjugate $\overline{9+9i}$ . . The conjugate of a complex number $a+bi$ is defined as $a-bi$ .
3. We need to find the product of the complex number and its conjugate.

STEP 2

First, we need to find the conjugate of the complex number $9+9i$ . As per the definition, the conjugate of a complex number $a+bi$ is $a-bi$ .
$\overline{9+9i} =9 -9i$

STEP 3

Now, we need to multiply the complex number $9+9i$ with its conjugate $9-9i$ .
$(9+9i)(9-9i)$

STEP 4

We will use the distributive property of multiplication over addition to multiply these two complex numbers.
$(9+9i)(9-9i) =9(9) +9(-9i) +9i(9) +9i(-9i)$

STEP 5

Now, simplify the multiplication.
$=81 -81i +81i -81i^2$

STEP 6

Note that $i^2$ is equal to $-1$ . So, replace $i^2$ with $-1$ .
$=81 -81(-1)$

STEP 7

Finally, simplify the expression to get the result.
$=81 +81 =162$ So, $(9+9i)(\overline{9+9i})=162$ .

Was this helpful?

Get Studdy

Scan QR code with your device to get Studdy on iOS or Android

QR code

Studdy solves anything!

Download the app

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Parents Influencer program Contact Policy Terms