SOLUTION: given that z1=2+i and z2=-3+4i and 1/z3=1/z1+1/z2. determine the value of z3 in standard form.

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Question 1206092: given that z1=2+i and z2=-3+4i and 1/z3=1/z1+1/z2. determine the value of z3 in standard form.
Found 3 solutions by mananth, Edwin McCravy, math_tutor2020:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!
given that z1=2+i and z2=-3+4i and 1/z3=1/z1+1/z2. determine the value of z3 in standard form.
z1=2+i
z2=-3+4i
= ............ (i^2=-i)


= ............ (i^2=-i)
(

Add take LCM











Simplify to get in standard form
z3=1.346+1.731i










Answer by Edwin McCravy(20056)   (Show Source): You can put this solution on YOUR website!
The other tutor got you here:



But don't go to rounded off decimals, 
as they aren't exact answers.

Reduce the fractions instead:



Then if you like, you can factor out 



Edwin
Answer by math_tutor2020(3817)   (Show Source): You can put this solution on YOUR website!

Answer:



Work Shown



Get every fraction on the right hand side in terms of the LCD



Apply reciprocal to both sides.



See scratch work section shown below.

Multiply top and bottom by conjugate of the denominator so the denominator becomes a real number.

Follow similar steps as the scratch work section shown below. Note: (a+bi)(a-bi) = a^2+b^2



Complex number is of the form a+bi where and

--------------------------------------------------------------------------

Scratch Work










Another approach for this scratch work section is to use the FOIL rule or the box method.
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