How do you write the trigonometric form into a complex number in standard form #1/4(cos225+isin225)#?

1 Answer
Jim G.
Aug 17, 2016

#-sqrt2/8-sqrt2/8 i#

Explanation:

Firstly, consider the trig part inside the bracket.

Now #225^@# is an angle in the 3rd quadrant where both the sin and cos ratios are #color(blue)"negative"#

#color(orange)"Reminder"#

#color(red)(|bar(ul(color(white)(a/a)color(black)(cos225^@=-cos(225-180)^@=-cos45^@)color(white)(a/a)|)))#

and #color(red)(|bar(ul(color(white)(a/a)color(black)(sin225^@=-sin(225-180)^@=-sin45^@)color(white)(a/a)|)))#

also #color(red)(|bar(ul(color(white)(a/a)color(black)(sin45^@=cos45^@=1/sqrt2)color(white)(a/a)|)))#

#rArrcos225^@+isin225^@=-1/sqrt2-1/sqrt2 i#

so now back to the original expression.

#1/4(cos225^@+isin225^@)=1/4(-1/sqrt2-1/sqrt2 i)#

distributing gives.

#-1/(4sqrt2)-1/(4sqrt2) i=-sqrt2/8-sqrt2/8 i" in standard form"#

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