# Math Help - imaginary numbers

1. ## imaginary numbers

(4 + 5i)^2 - (4 - 5i)^2
I have to write it in standard form a + bi

2. Originally Posted by aikenfan
(4 + 5i)^2 - (4 - 5i)^2
I have to write it in standard form a + bi
Difference of two squares,
(4+5i + 4 - 5i)(4+5i - 4 + 5i) = 8*10i = 0 + 80i

3. If $z = x + yi$ then
$z^2 - \overline z ^2 = \left( {z + \overline z } \right)\left( {z - \overline z } \right) = \left( {2x} \right)\left( {2yi} \right)
$
.

4. Originally Posted by aikenfan
(4 + 5i)^2 - (4 - 5i)^2
I have to write it in standard form a + bi
Foil it out:
$(4 + 5i)^2 - (4 - 5i)^2$

$= (16 + 40i + 25i^2) - (16 - 40i + 25i^2)$

$= 80i$

-Dan

5. Originally Posted by ThePerfectHacker
Difference of two squares,
(4+5i + 4 - 5i)(4+5i - 4 + 5i) = 8*5i = 0 + 40i
You sure?

6. Originally Posted by Krizalid
You sure?
Thank you I fixed it. I had too much to drink.

7. Thank you all very much! I've been working at that problem for the longest time but i just couldnt get it, but now i know what i was doing wrong! I forgot that it was squared when i copied it onto my paper