Consider the complex number = . z (a) (i) Find the modulus of z. (ii) Find the argument of giving your answer in radians. z, (4) (b) Using De Moivre’s theorem, show that is a cube root of one, = . z i.e. z (2) (c) Simplify (l + 2z)(2 + expressing your answer in the form + where z2), a bi, a and are exact real numbers. b
Consider the complex number z = . (a) (i) Find the modulus of z. (ii) Find the argument of z, giving your answer in radians. (4) (b) Using De Moivre’s theorem, show that z is a cube root of one, i.e. z = . (2) (c) Simplify (l + 2z)(2 + z2), expressing your answer in the form a + bi, where a and b are exact real numbers.
Complex-Nos-Revision-Sheet1.docx