Let z = 2 − 3i and w = 1 + i. Calculate the below:

(i) z − w; (ii) wz; (iii) z/w

(b) By converting 1 + √ 3i into polar form and applying de Moivre’s theorem, find real numbers a and b such that a + bi = (1 + √ 3i)^9

(c) Calculate all complex fourth roots of −i.

 

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De Moivre's Theorem (cos+isine)" = cos no+isinno for all positive integers n this extends to; e.g.(i) (1-i) [r(cos0+isin0)]" =r" (cosno+isinne) |2|=√√1²+(-1)² = √2 -[√xt() arg z = tan 11 R4 De Moivre's Theorem (cos+isine)" = cos no+isinno for all positive integers n this extends to; e.g.(i) (1-i) [r(cos0+isin0)]" =r" (cosno+isinne) |2|=√√1²+(-1)² = √2 -[√xt() arg z = tan 11 R4