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Express (2+j3)/(j(4-j5)) + 2/j in the form a+jb.
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Step-by-step solution
6 stepsHere's the solution to the problems.
: Express in the form .
Simplify the denominator of the first term and the second term.
For the first term's denominator:
For the second term:
Simplify the first term, , by multiplying the numerator and denominator by the conjugate of the denominator, which is .
Numerator:
Denominator:
So the first term simplifies to .
Add the simplified first term and the simplified second term.
The expression in the form is .
: If , express in the form .
Simplify the first term, , by multiplying the numerator and denominator by its conjugate, .
Simplify the second term, , by multiplying the numerator and denominator by its conjugate, .
Add the simplified first and second terms.
Combine the real parts and the imaginary parts:
Find a common denominator for the real parts (13 and 5, LCM is 65):
Find a common denominator for the imaginary parts (13 and 5, LCM is 65):
So, .
The expression for in the form is .
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