How do you add (-7-5i)(75i) and (-2+2i)(2+2i) in trigonometric form?

1 Answer
May 31, 2017

z=9.49(cos(18.43^@)+isin(18.43))z=9.49(cos(18.43)+isin(18.43)) or simply (9.49,18.43^@)(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+bia+bi or (a,b)(a,b)

(-7-5i)+(-2+2i)=(-7-2-5i+2i)=-9-3i(75i)+(2+2i)=(725i+2i)=93i

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

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

theta=tan^-1(b/a)=tan^-1((-3)/-9)=tan^-1(1/3)~~18.43^@θ=tan1(ba)=tan1(39)=tan1(13)18.43

r=sqrt(a^2+b^2)=sqrt((-9)^2+(-3)^2)=sqrt(90)~~9.49r=a2+b2=(9)2+(3)2=909.49

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