Answer:
B. -24
Explanation:
[tex](5+3i)(-2-4i)[/tex] expands to [tex]-10 -20i -6i - 12i^2[/tex]
i is the square root of -1, so the [tex]i^2[/tex] will simplify further and make the equation:[tex]-10 -20i-6i+12[/tex].
This can be simplified because there are 2 constants, -10 and +12, as well as 2 coefficients to the same variable.
So, the equation becomes:
[tex]2-26i[/tex]
The question asks of you, what is a+b from the parent expression a+bi.
b is the coefficient that is linked with the variable i.
a has no variable, so it must be the constant.
Here, the value of the "b" coefficient is -26. And the value of the constant is positive 2.
So we have to plug these 2 values into the equation a+b:
[tex]2+(-26)[/tex]
This solves out as, -24
So, the answer to this question is B.
The value of a + b for i = square root -1 is -24 (Option B)
To determine the value of a + b, we'll begin by obtaining the value of a and b. This can be obtained as illustrated below
(5 + 3i)(-2 - 4i) = a + bi
Expand
5(-2 - 4i) + 3i(-2 - 4i) = a + bi
-10 - 20i - 6i - 12i² = a + bi
-10 - 26i - 12i² = a + bi
But
i = √-1
i² = -1
Thus, we have:
-10 - 26i - 12(-1) = a + bi
-10 - 26i + 12 = a + bi
-10 + 12 - 26i = a + bi
2 - 26i = a + bi
From the above,
Therefore,
a + b = 2 + (-26)
a + b = 2 - 26
a + b = -24
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