5.52ELEMENTS OF MATHEMATICSAXEXERCISE 5.41. Find the modulusand princi

1.	5.52ELEMENTS OF MATHEMATICSAXEXERCISE 5.41. Find the modulusand principal argument of the following complex numbersthem in modulus amplitude form :3ii)) 2i
Answer» i) 1+√-3 = 1+ √3i , so modulus is √(1)²+(√3)² = √4 = 2. and argument is ∅ = tan^-1(√3/1) = π/3 ii) 1+i = modulus is √1²+1² = √2. and argument is ∅ = tan^-1(1/1) = π/4 iii) -2i , modulus is 2. and argument is -π/2.

5.52ELEMENTS OF MATHEMATICSAXEXERCISE 5.41. Find the modulusand principal argument of the following complex numbersthem in modulus amplitude form :3ii)) 2i

Answer»

i) 1+√-3 = 1+ √3i , so modulus is √(1)²+(√3)² = √4 = 2. and argument is ∅ = tan^-1(√3/1) = π/3

ii) 1+i = modulus is √1²+1² = √2. and argument is ∅ = tan^-1(1/1) = π/4

iii) -2i , modulus is 2. and argument is -π/2.