How do you write the trigonometric form in complex form #3/4(cos((7pi)/4)+isin((7pi)/4)))#?
1 Answer
Aug 10, 2016
Explanation:
Starting with the trig. part
That is
#cos((7pi)/4)+isin((7pi)/4)# Simplifying this as follows.
#color(orange)"Reminder"#
#color(red)(|bar(ul(color(white)(a/a)color(black)(cos((7pi)/4)=cos(2pi-(7pi)/4)=cos(pi/4)color(white)(a/a)|# and
#color(red)(|bar(ul(color(white)(a/a)color(black)(sin((7pi)/4)=-sin(2pi-(7pi)/4)=-sin(pi/4)color(white)(a/a)|)))#
#rArrcos((7pi)/4)+isin((7pi)/4)=cos(pi/4)-isin(pi/4)#
#color(orange)"Reminder" color(red)(|bar(ul(color(white)(a/a)color(black)(cos(pi/4)=sin(pi/4)=1/(sqrt2))color(white)(a/a)|)))#
#rArrcos(pi/4)-isin(pi/4)=1/sqrt2-1/sqrt2 i=sqrt2/2-sqrt2/2 i# Finally the whole expression becomes.
#3/4(sqrt2/2-sqrt2/2 i)=(3sqrt2)/8-(3sqrt2)/8 i" in complex form"#
