Test: Complex Numbers III - Ambitious

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Question 1:   Write the modified polar form of z=3( cos240°+isin240° ) using the shorthand notation
z=3 240°
z=3 120°
z=3 120°
z=3 240°
Question 2:   Write the proper polar form z=2( cos25°isin25° ) using the shorthand notation
3 25°
3 25°
2 335°
3 25°
Question 3:   Multiply the following: z 1 =x( cosθ+isinθ ) and z 2 =y( cosφ+isinφ )
z 1 z 2 =( x+y )( cos( θ+φ )+isin( θ+φ ) )
z 1 z 2 =xy( cos( θ+φ )+isin( θ+φ ) )
z 1 z 2 =xy( cos( θφ )+isin( θφ ) )
z 1 z 2 =xy( cos( θ+φ )isin( θ+φ ) )
Question 4:   Find z 1 z 2 , where z 1 =3( cos15°+isin15° ) and z 2 =5( cos63°+isin63° )
z 1 z 2 =8( cos78°isin78° )
z 1 z 2 =15( cos78°isin78° )
z 1 z 2 =15( cos78°+isin78° )
z 1 z 2 =8( cos78°+isin78° )
Question 5:   Find z 1 z 2 , where z 1 =4( cos31°+isin31° ) and z 2 =7( cos( 12° )+isin( 12° ) )
z 1 z 2 =28( isin43°cos43° )
z 1 z 2 =28( cos43°isin43° )
z 1 z 2 =11( cos19°isin19° )
z 1 z 2 =28( cos19°+isin19° )
Question 6:   Find z 1 z 2 , where z 1 =x( cosθ+isinθ ) and z 2 =y( cosφ+isinφ )
z 1 z 2 = x y ( cos θ φ +isin θ φ )
z 1 z 2 = x y ( cos( θφ )+isin( θφ ) )
z 1 z 2 =xy( cos( θφ )+isin( θφ ) )
z 1 z 2 = x y ( cos( θφ )isin( θφ ) )
Question 7:   Find z 1 z 2 , where z 1 =12( cos87°+isin87° ) and z 2 =4( cos29°+isin29° )
z 1 z 2 =8( cos56°isin56° )
z 1 z 2 =8( cos56°+isin56° )
z 1 z 2 =3( cos3°+isin3° )
z 1 z 2 =3( cos56°+isin56° )
Question 8:   Find z 1 z 2 z 3 , where z 1 =2( cos15°+isin15° ) , z 2 =3( cos16°+isin16° ) and z 3 =4( cos17°+isin17° )
z 1 z 2 z 3 =24( cos120°isin120° )
z 1 z 2 z 3 =9( cos48°+isin48° )
z 1 z 2 z 3 =24( cos48°+isin48° )
z 1 z 2 z 3 =24( cos120°+isin120° )
Question 9:   Find z n , where z=r( cosθ+isinθ )
z n = r n ( cos n θi sin n θ )
z n = r n ( cos n nθ+i sin n nθ )
z n =nr( ncosθ+insinθ )
z n = r n ( cosnθ+isinnθ )
Question 10:   Find z 3 , where z=3( cos25°+isin25° )
27( cos75°+isin75° )
27( 3cos25°+i3sin25° )
9( cos75°+isin75° )
27( cos 3 25°+i sin 3 25° )