Complex numbers questions | form six Pure Advanced Mathematics

(4106) Question Category: Mathematical Calculation

  1. Use Demoivre`s theorem to find the value of left ( frac{1}{2} + frac{1}{2}i ight )^{10}
  2. Show that  left [ r(cos heta +i,sin heta) ight ]^{n}=r^{n}e^{in heta} and hence find in form of re^{i heta} all complex numbers z, such that z^{3}=frac{5+i}{2+3i}
  3. i) Solve the equation x^{4}+1=0  and leave the roots in radical form.

          ii) If w=frac{z+2}{2} and |z|=4 , find the locus of the w.

Answer / Solution

UNSOLVED

(4945) Question Category: Mathematical Calculation

Express the complex number left ( frac{1+i}{1-i} ight )+left ( frac{sqrt{3}}{1-i} ight )^{4} in the form a+ib.

Answer / Solution

UNSOLVED

(4946) Question Category: Mathematical Calculation

Show  that [r(cos heta + isin heta )]^{n}=r^{n}e^{in heta}

Answer / Solution

UNSOLVED

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