What is the trigonometric form of # (5+i) #?

1 Answer
Jim G.
Jun 12, 2016

#sqrt26(cos(0.197)+isin(0.197))#

Explanation:

To convert a complex number into trig form.

#color(red)(|bar(ul(color(white)(a/a)color(black)(x+yi=r(costheta+isintheta))color(white)(a/a)|)))#
where r is the magnitude and #theta# the argument.

Since( 5 + i) is in the 1st quadrant the the following formulae allow us to calculate r and #theta#

#•r=sqrt(x^2+y^2#

#•theta=tan^-1(y/x)#

here x = 5 and y = 1

#rArrr=sqrt(5^2+1^2)=sqrt26#

and #theta=tan^-1(1/5)=0.197" radians""or11.3^@#

#rArr5+i=sqrt26(cos(0.197)+isin(0.197))#

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