Asked by 95
Find (-1+i)^1/3 list steps
Answers
Answered by
Reiny
At what level are you studying this?
Do you know DeMoivre's Theorem ?
Do you know DeMoivre's Theorem ?
Answered by
Reiny
change to polar form
r(cosØ + isinØ)
r = √(1+1) = √2
tan^-1 Ø = -1 (in II)
Ø = 135°
-1 + i = √2(cos135° + i sin135°)
(-1+i)^(1/3) = √2^(1/3)(cos 135/3 + i sin 135/3)
= 2^(1/6)(cos 45° + i sin 45°)
= 2^(1/6)(√2/2 + i√2/2)
= ( 2^(2/3) + i 2^(2/3) )/2
= 2^(-1/3) + i 2^(-1/3) or appr. .7937 + i(.7937)
check my arithmetic
r(cosØ + isinØ)
r = √(1+1) = √2
tan^-1 Ø = -1 (in II)
Ø = 135°
-1 + i = √2(cos135° + i sin135°)
(-1+i)^(1/3) = √2^(1/3)(cos 135/3 + i sin 135/3)
= 2^(1/6)(cos 45° + i sin 45°)
= 2^(1/6)(√2/2 + i√2/2)
= ( 2^(2/3) + i 2^(2/3) )/2
= 2^(-1/3) + i 2^(-1/3) or appr. .7937 + i(.7937)
check my arithmetic
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