Solution, Part (i)

`(-2+5j)/(-1-j) = (5.39 angle 112^text(o))/(1.41 angle 225^text(o))`

`=5.39/1.41angle(112^text(o)-225^text(o))`

`=3.82angle247^text(o)`

`=-1.49-3.52j`

Note: `112^"o" - 225^"o" = -113^"o"` is equivalent to positive `247^"o"`.

Part (ii) CHECK:

`(-2+5j)/(-1-j)`

`=((-2+5j)(-1+j))/((-1-j)(-1+j))`

`=(-3-7j)/2`

`=-1.5-3.5j`

Here's an explanation of what happened in the expansion of terms in the above answer.

The top of the fraction (the numerator) is:

(−2 + 5j)(−1 + j)

This gives us

−2(−1 + j) + 5j(−1 + j)

= 2 − 2j − 5j + 5j2

= 2 − 2j − 5j − 5

= −3 − 7j

The bottom part of the fraction is

(−1 − j)(−1 + j)

= (−1)2 − (j)2

= 1 − (−1)

= 1 + 1

= 2

[There is a rounding error in Part (i) since we used decimal approximations throughout. The answer in Part (ii) is exact.]

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