Complex numbers

Algebra Level 3

if ( x + i y ) ( 1 − i ) = 2 + i (x+iy)(1-i)=2+i , what is the value of x 3 + y 3 x^{3}+y^{3} ?


The answer is 3.50.

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Abdulrahman El Shafei by Abdulrahman El Shafei , 23, Egypt

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2 solutions

Mahmoud Mustafa
Jan 7, 2015

∵ ( x + i y ) ( 1 − i ) = x − i x + i y − i 2 y = x − i x + i y + y = 2 + i ∴ x + y = 2 , y − x = 1 ∴ 2 y = 3 ∴ y = 1.5 , x = . 5 ∴ x 3 + y 3 = . 5 3 + 1.5 3 = 3.5 T h i s i s m y f i r s t w r i t t e n s o l u t i o n o n B r i l l i a n t . \because (x+iy)(1-i)=x-ix+iy-{ i }^{ 2 }y=x-ix+iy+y=2+i\\ \therefore x+y=2\quad ,\quad y-x=1\\ \therefore 2y=3\\ \therefore y=1.5\quad ,\quad x=.5\\ \therefore { x }^{ 3 }+{ y }^{ 3 }={ .5 }^{ 3 }+{ 1.5 }^{ 3 }=3.5\\ This\quad is\quad my\quad first\quad written\quad solution\quad on\quad Brilliant\quad.

13 Helpful 0 Interesting 0 Brilliant 0 Confused

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Abdulrahman El Shafei - 6 years, 5 months ago

Congrats on your first written solution! Here's to many more!

Calvin Lin Staff - 6 years, 5 months ago

congrats! and thanx for the answer.........

Maitri Mishra - 6 years, 5 months ago
Prakriti Bansal
Jan 9, 2015

2 Helpful 0 Interesting 0 Brilliant 0 Confused

nice idea :)

Saleem Hd - 6 years, 4 months ago

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