SOLUTION: Write the complex number in polar form. 2 − 7i

Algebra ->  Trigonometry-basics -> SOLUTION: Write the complex number in polar form. 2 − 7i      Log On


   

Question 1204878: Write the complex number in polar form.
2 − 7i
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
The polar form of a complex number z+=+x+%2B+iy with coordinates (x, y) is given as:
z+=+r%2Acos%28theta%29%2B+i%2Ar%2A+sin%28theta%29+

where r+=+sqrt%28x%5E2+%2B+y%5E2%29+


given: 2+-+7i
x=2
y=-7
r+=+sqrt%28x%5E2+%2B+y%5E2%29+
r=sqrt%282%5E2%2B%28-7%29%5E2%29=sqrt%284%2B49%29=sqrt%2853%29
then
2-7i=sqrt%2853%29%2Acos%28theta%29%2Bi%2Asqrt%2853%29%2Asin%28theta%29

since theta=tan%5E-1%28y%2Fx%29=tan%5E-1%28-7%2F2%29=-tan%5E-1%287%2F2%29, we have

=>Answer