assignment5 - ma2176 a5 Complex Numbers 1. 2. Find the...

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1 ma2176 a5 Complex Numbers 1. Find the square roots of 51 2 i . 2. Simplify () 5 13 i −+ . 3. Find the modulus and argument of ( ) 2 11 3 1 ii i +− + . 4. If ω ( ) 1 is a complex cube root of unity, show that (a) ( )( ) 22 4 ωω +− = . (b) ( ) ( ) 66 2 5 2 2 2 5 729 ++ = = . 5. Find the modulus and argument of 1c o s s i n o s s i n i i θ when 0 π < < . What are the modulus and argument when 2 θπ < < ? 6. Solve the equation 4 zi += in the set of all complex numbers. 7. Solve the equation 642 10 zzz +++= . 8. Show that (a) 24 cos5 2 s i n 1 6 s i n cos =− + . (b) 43 64sin cos cos7 3cos3 3cos θθθ θθ =−− + . 9. (a) Solve the equation
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