How do you add #(-7-5i)# and #(-2+2i)# in trigonometric form?

1 Answer
Andy Y.
May 31, 2017

#z=9.49(cos(18.43^@)+isin(18.43))# or simply #(9.49,18.43^@)#

Explanation:

Strategy. First add them up, while they are still in rectangular form. Then convert the single term rectangular number into trigonometric form. Choose degrees or radians for the angle. I choose degrees.

Step 1. Add the two rectangular complex numbers. The result will be in standard rectangular form #a+bi# or #(a,b)#

#(-7-5i)+(-2+2i)=(-7-2-5i+2i)=-9-3i#

Here, #a=-9# and #b=-3#

Step 2. Given the conversion formulas, translate to trig form, which is of the form #z=r(cos(theta)+isin(theta))# or in polar form #(r,theta)#

#theta=tan^-1(b/a)=tan^-1((-3)/-9)=tan^-1(1/3)~~18.43^@#

#r=sqrt(a^2+b^2)=sqrt((-9)^2+(-3)^2)=sqrt(90)~~9.49#

#z=9.49(cos(18.43^@)+isin(18.43))# or simply #(9.49,18.43^@)#

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