Calculus Analyse lc-4, Complex Numbers Examples by Mejlbro L.

By Mejlbro L.

By Mejlbro L.

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Additional resources for Calculus Analyse lc-4, Complex Numbers Examples

Example text

Besides being a manager in the Manufacturing IT department, Kim performs triathlon at a professional level. ‘NNE Pharmaplan offers me freedom with responsibility as well as the opportunity to plan my own time. com NNE Pharmaplan is the world’s leading engineering and consultancy company focused exclusively on the pharma and biotech industries. NNE Pharmaplan is a company in the Novo Group. 13 Let a = b be complex numbers, and let k be a positive real number, k = 1. Prove that {z ∈ C | |z − a| = k · |z − b|} describes a circle in the complex plane.

Let 2 + i = a + ib, where a and b ∈ R. e. a2 + b2 = √ 5 and from previously a2 − b2 = 2. This gives √ a=± 5+2 , 2 √ b=± 5−2 , 2 ab > 0, hence, √ 2+i=± ⎧ ⎨ ⎩ √ 5+2 +i 2 √ ⎫ 5 − 2⎬ . 2 ⎭ We can therefore write the four roots, −1 + √ 5+2 +i 2 √ 5−2 , 2 −1 + √ 5−2 −i 2 √ 5+2 , 2 √ −1 − √ −1 − 5+2 −i 2 √ 5−2 , 2 5−2 +i 2 √ 5+2 . 6 Let ± w denote the two solutions of the equation z 2 = w. Find the values of the following expressions written in the form a + ib: √ 1) ± 1 + i, √ 2) ± 1 ± i, √ 3) ± ± i. A.

Com NNE Pharmaplan is the world’s leading engineering and consultancy company focused exclusively on the pharma and biotech industries. NNE Pharmaplan is a company in the Novo Group. 13 Let a = b be complex numbers, and let k be a positive real number, k = 1. Prove that {z ∈ C | |z − a| = k · |z − b|} describes a circle in the complex plane. Specify the centre and the radius of the circle. A. Point set in the complex plane. D. Square the condition and then reduce. I. The condition is equivalent to |z − a|2 = k 2 |z − b|2 .