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Express (1+7i) in Eulerian form. |
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Answer» Answer: The expression is euler formula is given as √50 ( cos(81. 86) + i son (81.86). Step-by-step explanation: To solve: Express (1+7i) in EULERIAN form. According to Eulerian formula, a+bi = rcos θ + r i sin θ 1+7i = r cos θ + r i sinθ Thus rcos θ = 1 r sinθ = 7 r = √(1) ^2+ (7) ^ r = √ 1+49 r = √50 rcos θ = 1 Hence, cos θ = 1/r = 1/√50 Hence, θ = 81.86 Also, r sinθ = 7 Hence, sinθ = 7/r sinθ = 7/√50 Hence, θ = 81.86 Euler form is EXPRESSED as a+bi = rcos θ + r i sin θ 1+7i = r (cos θ + i sin θ) = √50 ( cos(81. 86) + i son (81.86) Hence, the expression is euler formula is given as √50 ( cos(81. 86) + i son (81.86) |
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