How do you convert 1 + 4i1+4i to polar form?

1 Answer
May 15, 2016

~=sqrt(17)(cos1.33 + isin1.33)17(cos1.33+isin1.33)

Explanation:

If z = a +biz=a+bi

Then zz may be expressed in polar form as:

z = r(cos theta + i sin theta)z=r(cosθ+isinθ)
Where: r = sqrt(a^2 + b^2)r=a2+b2 and theta = arctan(b/a)θ=arctan(ba)

In this example: z=1+4iz=1+4i
Hence: a=1a=1 and b=4b=4

Therefore: r = sqrt(1^2+4^2)r=12+42 =sqrt(17)17
And: theta = arctan(4/1)θ=arctan(41) ~= 1.331.33

Hence: z ~= sqrt(17)(cos 1.33 + i sin 1.33)z17(cos1.33+isin1.33)