How do you convert #3+ j5# to polar form?

1 Answer
Jim G.
Sep 6, 2016

#(sqrt34,1.03)#

Explanation:

To convert from #color(blue)"cartesian to polar form"#

That is #(x,y)to(r,theta)#

#color(orange)"Reminder " color(red)(|bar(ul(color(white)(a/a)color(black)(r=sqrt(x^2+y^2))color(white)(a/a)|)))#

and #color(red)(|bar(ul(color(white)(a/a)color(black)(theta=tan^-1(y/x))color(white)(a/a)|)))#

here x = 3 and y = 5

#rArrr=sqrt(3^2+5^2)=sqrt(9+25)=sqrt34#

Now 3 + 5j is in the 1st quadrant so we must ensure that #theta# is in the 1st quadrant.

#theta=tan^-1(5/3)=1.03" radians"larr " in 1st quadrant" #

Thus #(3,5)to(sqrt34,1.03)to(sqrt34,59.04^@)#

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