Question
The complex number
is given by
, what is
the polar representation of
?
Select one:
a.
b.
c.
d.
the polar representation of
Select one:
a.
b.
c.
d.
Ask by Summers Malone. in Ghana
Mar 15,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The polar representation of
is
.
Solution
We are given
.
-
Compute the modulus
: -
Compute the argument
: -
Write the polar representation:
The correct answer is:
d. .
d.
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Beyond the Answer
To find the polar representation of the complex number
, we need to determine its magnitude
and angle
.
-
The magnitude
is given by: -
The angle
is obtained using the arctangent function:
Now, expressing
in polar form:
Therefore, the correct answer is:
d. .
d.
Now, let’s add some fun facts!
In ancient history, the concept of complex numbers was largely ignored until the 16th century when it became useful in solving cubic equations. Mathematicians like Gerolamo Cardano began incorporating imaginary numbers into their calculations, paving the way for modern mathematics!
Want to impress your friends? Try explaining that complex numbers have real-world applications in electrical engineering! Engineers use them to analyze AC circuits by representing voltage and current as complex numbers, making it easier to understand phase differences and oscillations! Who knew math could be so cool?