Question

I really really need help with this and no one is answering. I've looked everywhere for how to do this and I fell like its simple but I can't find it. given -2+4i, express the complex number in polar form. I know the answer is 2 root 5(cos2.03 + isin2.03), but I don't know where the 2.03 comes from. Can someone explain please?

Answer 1

Step-by-step explanation:

a+bi = -2+4i

arctan(b/a)=arctan(4/-2)=-1.071

Because this falls in quardant 2, you have to add pi

1.071+pi=2.03

I hope this helps.

Answer 2

Result:

Complex number:

The polar form of z is:

Step-by-step explanation:

z = −2 + 4i

z = 4.4721 · (cos 117o + i · sin 117o)

The polar form of the complex number z = a + bi is:

z = r · (cos θ + i · sin θ)

where, r is the modulus of z and θ is an argument of z. The moduo for a = −2 and b = 4 is:

r = a2 + b2 = · · · = 4.4721 To find argument θ we use one of the following formulas:

b θ=arctan a ifa>0

b o θ=arctan a +180 ifa<0

θ=90o ifa=0andb>0 θ=270o ifa=0andb<0

Inthisexample: a=−2andb=4so:

θ=arctan a +180

θ=arctan 4 +180o −2

b o

θ = arctan (−2) + 180o θ ≈ 117o

Try this website it’s really helped me!

www.mathportal.org/calculators/complex-numbers-calculator/complex-unary-operations-calculator.php?val1=-2&combo1=1&val2=4&rb1=pol&ch2=useDecimals