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spayn [35]
3 years ago
6

If i^2=-1 and (4+2i)(6-ki)=30, what is the value of k?

Mathematics
1 answer:
ZanzabumX [31]3 years ago
6 0
I^2 = -1
i = √-1

Substitute the value of i in the equation:
(4+2i)(6-ki)=30
{4 + (2)(√-1)} {6 - k (√-1)} = 30
( 4 + 2√-1)(6 -k√-1) = 30
24 - 4k√-1 + 12√-1 -2k (-1) =30
24 - 4k√-1 + 12√-1 +2k =30
-4k√-1+12√-1 + 2k - 6 =0
-2√-1(2k -6) + (2k-6) =0
(-2√-1 +1)(2k-6)=0

2k -6 =0
2k = 6
k= 3

So, the value of k is 3.
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