View attached explanation and answer. Let me know if you have any questions.

ANSWERS
Q1.

Short answers.

1.1

Simplified form of

−25 + 3 −4 + 2 −9

−25 + 3 −4 + 2 −9 = 5i + 3 ( 2i ) + 2 ( 3i ) = 17i
1.2

Polar form of 0 + i
Let z = 0 + i

r = z = 02 + 12 = 1


1
 = tan −1   = 90 = rad
0
2
 



1.3

Let

z = (1 + i )

2

Then

( ) = (1− i )

z = (1 + i ) = 1 + i
2



i
i
 
 
z = rei = 1e 2 = e 2 = cos   + i sin  
2
2

Polar form:

2

2

OR

z = 1 + 2i + i 2 = 1 + 2i − 1 = 0 + 2i

z = 0 + 2i = 0 − 2i = −2i
1.4

The dot product

1, −2,3  −1,2,2 = −1 − 4 + 6 = 1
1.5

a = 2i + 2 j − 3k

3a = 3 a = 3 22 + 22 + ( −3) = 3 4 + 4 + 9 = 3 17
2

Q2.

Short answers.

2.1

To find x and y:

( −2 + i ) x + 2 y = 1 + 3i
−2 x + xi + 2 y = 1 + 3i

( −2 x + 2 y ) + xi = 1 + 3i
Equating real and imaginary parts:

 −2 x + 2 y = 1

x=3

Solving above, we get:

x = 3,
2.2

y=

7
2

Cartesian Form

( 260 ) + (130 ) = 2 ( cos 60 + i sin 60 ) + 1( cos3...