Question 1021320
i believe this is what you are looking for.


<a href = "http://www.regentsprep.org/regents/math/algtrig/ato6/absvlecomlesson.htm" target = "_blank">http://www.regentsprep.org/regents/math/algtrig/ato6/absvlecomlesson.htm</a>


let's do them in turn.


remember the general form is a + bi.
this can also be shown as a + ib, as in some of your problems.
a is the real part.
b is the coefficient of the imaginary part.


the absolute value is equal to sqrt(a^2 + b^2).


your first one is:


1) -2 + i * sqrt(10) 


a = -2
b = sqrt(10)


sqrt(a^2 + b^2) = sqrt(4 + 10) = sqrt(14)


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2) 3 - i * sqrt (5) 


a = 3
b = -sqrt(5)


sqrt(a^2 + b^2) = sqrt(9 + 5) = sqrt(14)


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3) - sqrt(9) - 2i


a = sqrt(9)
b = -2


sqrt(a^2 + b^2) = sqrt(9 + 4) = sqrt(13)


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4) 2 + 3i 


a = 2
b = 3


sqrt(a^2 + b^2) = sqrt(4 + 9) = sqrt(13)


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5) sqrt(6)-3i


a = sqrt(6)
b = -3


sqrt(a^2 + b^2) = sqrt(6 + 9) = sqrt(15)


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your solutions are:


1.  sqrt(14)
2.  sqrt(14)
3.  sqrt(13)
4.  sqrt(13)
5.  sqrt(15)


looks like the last one is the biggest.


looks like you did some of the calculations  correctly.