Question
What is the real part of the number $5i$?
This question was previously asked in
RRB ALP/Technician 2018 CBT 2 Electronics Mechanic Question Paper (23-Jan-2019) (Shift 1)
The correct answer is
0
Understanding the Real Part of a Complex Number
A complex number is generally expressed in the standard form a + bi, where:
- a is the real part.
- b is the imaginary part.
- i is the imaginary unit, defined as $i = \sqrt{-1}$.
Identifying the Real Part of $5i$
The given number is $5i$. This is a purely imaginary number.
To find its real part, we can write $5i$ in the standard form a + bi:
$5i = 0 + 5i$
Comparing $0 + 5i$ to the standard form a + bi:
- The value of a (the real part) is 0.
- The value of b (the imaginary part) is 5.
Therefore, the real part of the number $5i$ is 0.
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Important Questions from Complex Numbers
- Consider the following complex numbers
$$ z_1 = r_1(\cos \theta_1 + i \, \sin \theta_1) $$
$$ z_2 = r_2(\cos \theta_2 + i \, \sin \theta_2) $$
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