ShaveTheWhales ShaveTheWhales

02-05-2017
Mathematics

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Simplify the complex number. Express your answer in a + bi form and include each step necessary in simplifying.[tex] \frac{3-2i}{1+4i} [/tex]

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LammettHash LammettHash

02-05-2017

[tex]\dfrac{x+iy}{u+iv}\times\dfrac{u-iv}{u-iv}=\dfrac{(x+iy)(u-iv)}{u^2-(iv)^2}[/tex]
[tex]=\dfrac{xu-i^2yv+iyu-ixv}{u^2+v^2}[/tex]
[tex]=\underbrace{\dfrac{xu+yv}{u^2+v^2}}_a+i\underbrace{\dfrac{yu-xv}{u^2+v^2}}_b[/tex]

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