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adoni [48]
3 years ago
8

What is the polar form of -4+5i?

Mathematics
1 answer:
kifflom [539]3 years ago
5 0

z= r(cosθ+i sinθ) is the required polar form where, r = √41 and θ =π- tan^{-1} (\frac{5}{4} )

Step-by-step explanation:

Given,

-4+5i is a complex number.

To find the polar form.

Formula

z=x+iy

r² = mod of (x²+y²)

θ = tan^{-1} (\frac{y}{x} )

So, the polar form will be z=r(cosθ+i sinθ)

Now,

r² =(-4)²+5² = 41

or, r = √41

θ =π- tan^{-1} (\frac{5}{4} ) [ since the point is in second quadrant]

Hence,

z= r(cosθ+i sinθ) is the required polar form where, r = √41 and θ =π- tan^{-1} (\frac{5}{4} )

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