Help!!!! Pre calc homework

Question

Please help I need this complex number expressed in polar form

(-5)-2i

Answer 1

Stephanie,

 

The complex number z=-5-2i can be though of as a vector in 2 dimensions with an x component of -5 and a y component of -2. If you plot this point you will see that it falls in the third quadrant. To express this in polar form r,θ first calculate r=(5²+2²)^1/2=5.38... and θ= tan^-1(2/5)=21.801 deg. in the third quadrant add 180=201.801 deg from the positive x axis then z can be expressed as z=r(cosθ + i*sinθ) 

Hope this helps

Jim

 

 

Answer 2

 In polar form       r (cosθ+i sinθ)

where r =√(a² +b²)   and  θ= tan¯ ¹(b/a)  

 

comparing with a+ib we have    a= -5    and    b= -2

 

now r=√[(-5)² +(-2)²]  =√(25+4) = √(29)

 

and θ=tan¯ ¹(-2/-5) =tan¯ ¹(2/5)

 

 

so complex no. in polar form...put the values of r and  θ and find it out.