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Find the positive value of t that satisfies ab = t - 2i given |a| = 2 and |b| = sqrt(26).

 Oct 20, 2019
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AB = T - 2i

|A| = 2, |B| = sqrt(26)

 

First, let's assume that A and B are positive values

 

2sqrt(26) = T - 2sqrt(-1)

T = 2(sqrt(26) + i)

 

Then, assuming A and B are negative values

 

(-2)(-1)sqrt(26) = T - 2i

2sqrt(26) = T -2sqrt(-1)

 

They are the same thing. Ergo, the value of T is 2(sqrt(26) + i) OR 2sqrt(26) + 2i. Whichever way you want to present it.

 Oct 20, 2019

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