Write the following complex number in polar form. Express all angles in degrees rounded to the nearest tenth.
Given complex number: 5+6i
nope.
sqrt(61) @50.2
r^2 = 5^2 + 6^2
r = ...
tanØ = 6/5
Ø = appr 50.2° or .88 radians
put it all together
r=61 and
TanØ= 50.2°
so it would be like
61(cos5.2+isin5.2)?
In my exercises, the only answer appears as 61(cos5.2+isin5.2) and sqrt61(cos5.2+isin5.2)
To express a complex number in polar form, we need to find its magnitude (or modulus) and argument (or angle).
The magnitude of a complex number is given by the formula:
|z| = √(a^2 + b^2)
where a and b are the real and imaginary parts of the complex number respectively.
In this case, the real part (a) is 5, and the imaginary part (b) is 6. Plugging these values into the formula, we get:
|z| = √(5^2 + 6^2)
= √(25 + 36)
= √(61)
≈ 7.8
The argument of a complex number can be found using the formula:
arg(z) = atan(b/a)
where atan is the inverse tangent function.
In this case, plugging in the values, we get:
arg(z) = atan(6/5)
≈ 50.2 degrees
Therefore, the given complex number 5+6i can be expressed in polar form as approximately 7.8 ∠ 50.2°.