eiaW8infYokochr
eiaW8infYokochr eiaW8infYokochr
  • 15-08-2016
  • Mathematics
contestada

Find (–1 –i sqrt(3))^10 .Express in rectangular form.

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HomertheGenius
HomertheGenius HomertheGenius
  • 18-08-2016
z = - 1 - i√3
x = - 1, y = -√3
r = |z| = √ ( -1)² + (-√3)² = √( 1 + 3 )= √4 = 2
Ф = arc tan ( -√3/-1 ) = arc tan (√3 ) = 60° = π/3 
r ^n ( cos nФ + i sinФ ) = 2^10 ( cos (10π/3) + i sin (10π/3) )=
= 2^10( -1/2 - i √3/2 ) = 2^9( - 1 - i √3 )
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