# SOLUTION: What do you call this formula z=|z| (cos&#1138; + sin&#1138;)? And please tell more 'bout it.

Algebra ->  Algebra  -> Trigonometry-basics -> SOLUTION: What do you call this formula z=|z| (cos&#1138; + sin&#1138;)? And please tell more 'bout it.      Log On

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 Algebra: Trigonometry Solvers Lessons Answers archive Quiz In Depth

 Question 476982: What do you call this formula z=|z| (cosѲ + sinѲ)? And please tell more 'bout it.Answer by Edwin McCravy(8921)   (Show Source): You can put this solution on YOUR website!```You left out the i. It's z = |z|(cosѲ + i·sinѲ) That's the trigonometric form of the complex number z = x + iy The complex imaginary number z = x + yi is represented by the vector (line segment) from the origin to the point (x,y). So we draw and arbritrary point (x,y). (x,y) could be in any quadrant or even on an axis, but we'll draw it in the first quadrant. We'll label the length of the vector from the origin to the point (x,y) as |z|. Now from the point (x,y) we drop a perpendicular to the x-axis (in green): That makes a right triangle. The base of that right triangle is the same as the x-coordinate of the point (x,y), so it is x. The green side of that right triangle is the same as the y-coordinate of the point (x,y), so it is y. The angle that the vector makes with the x-axis is labeled Ѳ. So from the triangle, which gives and which gives Therefore Then we can factor out the and get That's the trigonometric or "trig" form of the complex number x+iy. It allows us to bring trig into the algebra of complex numbers. It will make certain operations simpler. Edwin```