Question

Find the conjugate of

7-3i
8+2i

Find the product and conjugate of
4-i
6+3i

(I am not asking for just the answer I would also like to know how you got that answer)

Answer 1

#1

• z=7-3i

`\\ \sf\longmapsto \overline{z}=7+3i`

#2

• z=8+2i

`\\ \sf\longmapsto \overline{z}=8-2i`

#3

`\boxed{\sf z\overline{z}=|z|^2}`

`\\ \sf\longmapsto z=4-i`

`\\ \sf\longmapsto |z|^2=4^2+(-1)^2`

`\\ \sf\longmapsto 16+1=17`

#4

`\\ \sf\longmapsto |z|^2`

`\\ \sf\longmapsto 6^2+3^2`

`\\ \sf\longmapsto 36+9`

`\\ \sf\longmapsto 45`

Answer 2

see below

Explanation:

To find the conjugate of a+bi take the opposite of bi so it would be a - bi

7-3i, the conjugate is 7 + 3i

8+2i the conjugate is 8 -2i

The product of a number and its conjugate is

(a+bi) (a-bi) = a^2 +abi-abi -b^2 i^2 = a^2 - b^2 (-1) = a^2 + b^2

( 4-i) ( 4+i) = 4^2 + 1^2 = 16+1 = 17

( 6+3i)(6-3i) = 6^2 + 3^2 = 36+9 = 45