(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show this by writing the individual factors on the left in exponential form, performing the needed operations, and finally changing back to rectangular coordinates.

2. Relevant equations

i is an imaginary number.

3. The attempt at a solution

Looking at the numerator, z_1 = 5i where r = |z_1|= 5, theta = pi/2.

Looking at the denominator, z_2 = 2+i where r = |z_2| = sqrt(5), theta = arctan(1/2).

So, in exponential form, 5i/(2+i) becomes 5*e^(i*pi/2) / sqrt(5)*e^(i*arctan(1/2)) =>

sqrt(5)*e^(i*pi/2) / e^(i*arctan(1/2)) = sqrt(5)*e^(i*((pi/2) - arctan(1/2))) but I don't see how this can be turned back into 1+2i since 1+2i in exponential form

is sqrt(5)*e^(i*arctan(2)).

Am I missing an algebra step or did I do something wrong?

Thank you.

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# Show 5i/(2+i) = 1+ 2i

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