Can I add a photo here because I don't know how to ask a question in math
2 answers:
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The value 18 will go in the first box
For the next two boxes, you'll type in
or (16/63)pi or something along those lines. The answer format will vary depending on how your teacher wants it.
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To get those values, I used the rule
If
z = a*(cos(b) + i*sin(b)) and w = c*(cos(d)+i*sin(d))
then
z*w = a*c*(cos(b+d)+i*sin(b+d))
In this case
a = 2
c = 9
so a*c = 2*9 = 18 goes in that first box
Then we compute b+d
b+d = (pi/9) + (pi/7)
b+d = (7pi)/63 + (9pi)/63
b+d = (16/63)pi
which goes in the last two boxes
For the next two boxes, you'll type in
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To get those values, I used the rule
If
z = a*(cos(b) + i*sin(b)) and w = c*(cos(d)+i*sin(d))
then
z*w = a*c*(cos(b+d)+i*sin(b+d))
In this case
a = 2
c = 9
so a*c = 2*9 = 18 goes in that first box
Then we compute b+d
b+d = (pi/9) + (pi/7)
b+d = (7pi)/63 + (9pi)/63
b+d = (16/63)pi
which goes in the last two boxes