What is the trigonometric form of # (2+5i) #?

1 Answer
Trevor Ryan.
Mar 29, 2016

#sqrt29 /_1.19#

Explanation:

Any complex number #z=x+iy# in rectangular form, may be written in polar form #z=r/_theta# by making use of the transformations:
#r=sqrt(x^2+y^2)and theta=tan^(-1)(y/x), theta in [-pi,pi]#.

So in this particular case, since the complex number is in the first quadrant of the argand plane, we get:

#r=sqrt(2^2+5^2)=sqrt29#

#theta=tan^(-1)(5/2)=68,2^@=1.19rad#.

Thus the point may be represented as #sqrt29 /_1.19#

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