Diverted Vieta
If and , find . Round off your answers to four decimal places.
The answer is 12.5992.
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1 solution
( m + 2 i n ) 3 = m 3 + 6 i m 2 n − 1 2 m n 2 − 8 i n 3 = 4 0 − 2 0 i , w h e r e i = − 1 Multiplying both sides with their complex conjugates, we get ( m 2 + 4 n 2 ) 3 = 4 0 2 + 2 0 2 = 2 0 0 0 . Answer is 2 0 0 0 3 1 ≈ 1 2 . 5 9 9 2 .