Test: Complex Numbers II - Ambitious

Double click on maths expressions to zoom
Question 1:   If ( x+y )+( xy )=5+3i , find x and y
x=2,y=0
x=3,y=2
x=4,y=1
x=5,y=3
Question 2:   Express z=6+8i in the polar form
z=10( sin53.13°+icos53.13° )
z=10( cos53.13°+isin53.13° )
z=14( cos36.87°+isin36.87° )
z=10( cos36.87°+isin36.87° )
Question 3:   Express z=4+3i in the shortened polar form
z=7 36.87°
z=4 36.87°
z=5 53.13°
z=5 36.87°
Question 4:   Express z=45i in the shortened polar form
z=6 231.34°
z=9 51.34°
z= 41 51.34°
z= 41 231.34°
Question 5:   Express 3( cos15°+isin15° ) in the form a+ib
3+i
2.898+0.777i
1.4572.721i
0.551+0.289i
Question 6:   Express 7( cos32°+isin32° ) in the form a+ib
3.71+5.936i
5.936+7i
7+2.56i
5.936+3.71i
Question 7:   Express 5 237° in the form a+ib
1.625+2.785i
2.7254.195i
1.575+3.642i
4.3953.115i
Question 8:   Change 3 60° to the exponential form
3 e π 3 i
3 e π 3 i
3 e π 2 i
6 e πi
Question 9:   Change 12 210° to the exponential form
12 e 6 7 πi
6 e 5 6 πi
12 e 5 6 πi
12 e 7 6 πi
Question 10:   Change 7 197.5° to the exponential form
6 e 19 18 πi
7 e 79 72 πi
12 e 1.2πi
12 e 19 18 πi