To determine the polar form of a complex number, we need to express it in terms of its magnitude (or modulus) and argument (or angle).
Given the complex number Z1 = 5 + 2i, we can calculate its magnitude (r) and argument (θ) using the following formulas:
Magnitude (r): r = √(a^2 + b^2)
Argument (θ): θ = arctan(b/a)
Where a is the real part (5) and b is the imaginary part (2) of the complex number.
Calculating the values:
Magnitude (r): r = √(5^2 + 2^2) = √29
Argument (θ): θ = arctan(2/5)
Using a calculator, we can find that θ is approximately 0.3805 radians or approximately 21.80 degrees (rounded to two decimal places).
Therefore, the polar form of Z1 = 5 + 2i is r ∠ θ, where r is approximately √29 and θ is approximately 0.3805 radians (or approximately 21.80 degrees).