What is the trigonometric form of # (7-i) #?

1 Answer
Aug 18, 2016

#5sqrt2(cos(0.142)-isin(0.142))#

Explanation:

To convert from #color(blue)"complex to trigonometric form"#

That is #(x+yi)to[r(costheta+isintheta)]" where"#

#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)|)))#

For (7 - i) , x = 7 and y = - 1

#rArrr=sqrt(7^2+(-1)^2)=sqrt50=5sqrt2#

Now (7 - i) is in the 4th quadrant, so we must ensure that #theta# is in the 4th quadrant.

#theta=tan^-1(-1/7)=-0.142" in 4th quadrant"#

#rArr(7-i)=5sqrt2(cos(-0.142)+isin(-0.142))#

#color(orange)"Reminder"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(cos(-theta)=costheta" and " sin(-theta)=-sintheta)color(white)(a/a)|)))#

#rArr(7-i)=5sqrt2(cos(0.142)-isin(0.142))#