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jiteshmeghwal9
 one year ago
If\[z_1=2+3i\]\[z_2=1+2i\]then
\[z_1z_2z_1^3=?\]
jiteshmeghwal9
 one year ago
If\[z_1=2+3i\]\[z_2=1+2i\]then \[z_1z_2z_1^3=?\]

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Empty
 one year ago
Best ResponseYou've already chosen the best response.1Give it your best try and show your steps

jiteshmeghwal9
 one year ago
Best ResponseYou've already chosen the best response.1\[z_1.z_2=(2+3i)(1+2i)\]\[z_1z_2=(26)+i(4+3)\]\[z_1z_2=4+7i\]now\[z_1^3=8+27i^3+54i^2+36i\]\[z_1^3=46+27i^3+36i\]\[z_1z_2z_1^3=4229i+27i^3\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Nice! \(i^3\) simplifies further right ?

Empty
 one year ago
Best ResponseYou've already chosen the best response.1It looks almost right, except you seem to have messed up your terms here: \(z_1^3 = 8 + 12i + 18i^2 + 27i^3\) Which can also be simplified further with @ganeshie8 's comment. :D

jiteshmeghwal9
 one year ago
Best ResponseYou've already chosen the best response.1\(4229i27i\)=\(4256i\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2dw:1440491573056:dw

Empty
 one year ago
Best ResponseYou've already chosen the best response.1The picture is nice since all a cube power means is multiply something by itself three times, \(i^3 = i*i*i\) So simplifying this should be no big deal, since you know what \(i*i=1\) already.

jiteshmeghwal9
 one year ago
Best ResponseYou've already chosen the best response.1the answer given in book is \(422i\). nt matching :/

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2http://www.wolframalpha.com/input/?i=%282%2B3i%29*%281%2B2i%29%282%2B3i%29%5E3

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2must be an algebra error somewhere, just double check..

jiteshmeghwal9
 one year ago
Best ResponseYou've already chosen the best response.1yes\[z_1z_2z_1^3=4229i27i^3\]\[=4229i+27i=422i\]

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2In case this is first time, it might be a bit exciting to notice that any power of \(i\) always simplifies to one of the numbers : \(\{\pm 1, ~\pm i\}\)

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2This holds : \[\large i^{n}\equiv i^{n\pmod{4}}\] In other words, subtracting/adding \(4\) from the exponent doesn't change the number
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