Question

The imaginary part of(3÷2+√5i÷3)^2

Answer 1

Answer:

z=

2i−1

3i

20

−i

19

=

2i−1

3(1)−(−i)))

=

−1+2i

3+i

=

−1+2i

3+i

×

−1−2i

−1−2i

=

(−1

2

)+2

2

−3−6i−i−2i

2

=

5

−1−7i

=

5

−1

−

5

7

i

Re(z)=−

5

1

and Im(z)=

5

−7

Answer 2

Step-by-step explanation:

(3/2+√5i/3)^2

(3/2)^2+(√5i/3)^2+2.3/2.√5i/3

9/4+5i^2/9+√5i

9/4+5×(-1)/9+√5i

9/4-5/9+√5i

81-20/36+√5i

61/36+√5i

Therefore the imaginary part is √5i