Consider the complex number z $=$ i$(5+7$i$).$ Recall that i is the imaginary unit, where i$2=1.$

$($a$)$ Consider the following commands.

$($i$)$

z$=$complex$(0,1)*$complex$(5,7)$

$($ii$)$

z$=$complex$(5,-7)$

$($iii$)$

z$=5$j$-7$

$($iv$)$

z$=$j$(5+7$j$)$

Determine which of the above commands gives a correct representation $(1)$ or NOT correct representation $(2)$ of the above complex number z$.$

So$,$ for example, if you think that the answers, in the above order, are Correct,Not Correct,Not Correct,Correct then you would enter $\text{'}1,2,2,1\text{'}$ into the answer box below $($without the quotes$).$

$($b$)$ Consider the following commands.

$($i$)$

z$=-7+5*$j

$($ii$)$

z$=$complex$(-7,5)$

$($iii$)$

z$=1$j$*(5+7$j$)$

$($iv$)$

z$=$j$*(5+7*$j$)$

Determine which of the above commands gives a correct representation $(1)$ or NOT correct representation $(2)$ of the above complex number z$.$

So$,$ for example, if you think that the answers, in the above order, are Correct,Not Correct,Not Correct,Correct then you would enter $\text{'}1,2,2,1\text{'}$ into the answer box below $($without the quotes$).$