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Q6:
Express the complex number 
in the form $a + ib$.
Express the complex number in the form $a + ib$.
Solution :
Given Expression
The expression to be simplified is:
$z = \left( \frac{1}{5} + i \frac{2}{5} \right) - \left( 4 + i \frac{5}{2} \right)$
Step 1: Distributing the Negative Sign
To perform complex subtraction, we treat the real and imaginary components separately. We distribute the negative sign across the second parenthesis [Per the Associative and Distributive Properties of Complex Numbers]:
$z = \left( \frac{1}{5} + i \frac{2}{5} \right) - 4 - i \frac{5}{2}$
Step 2: Grouping Real and Imaginary Components
We rearrange the expression to isolate real terms ($a$) and imaginary terms ($ib$):
$z = \left( \frac{1}{5} - 4 \right) + i \left( \frac{2}{5} - \frac{5}{2} \right)$
Step 3: Calculating Real and Imaginary Parts
For the real part ($a$):
$a = \frac{1}{5} - \frac{20}{5} = -\frac{19}{5}$
For the imaginary part ($b$):
Finding a common denominator of 10:
$b = \left( \frac{2 \times 2}{5 \times 2} - \frac{5 \times 5}{2 \times 5} \right) = \left( \frac{4}{10} - \frac{25}{10} \right) = -\frac{21}{10}$
Visual Representation of the Complex Number in the Argand Plane
Step 4: Final Formatting
Combining the calculated real and imaginary coefficients into the standard form $z = a + ib$:
$z = -\frac{19}{5} + i \left( -\frac{21}{10} \right)$
Final Solution: $-\frac{19}{5} - \frac{21}{10}i$
More Questions from Class 11 Mathematics Complex Numbers EXERCISE 4.1
- Q1: Express the complex number in the form $a + ib$.
- Q2: Express the complex number $i^9 + i^{19}$ in the form $a + ib$.
- Q3: Express the complex number $i^{-39}$ in the form $a + ib$.
- Q4: Express the complex number $3(7 + i7) + i(7 + i7)$ in the form $a + ib$.
- Q5: Express the complex number $(1 - i) - (-1 + i6)$ in the form $a + ib$.
- Q7: Express the complex number in the form $a + ib$.
- Q8: Express the complex number $(1 - i)^4$ in the form $a + ib$.
- Q9: Express the complex number in the form $a + ib$.
- Q10: Express the complex number in the form $a + ib$.
- Q11: Find the multiplicative inverse of the complex number $4 - 3i$.
- Q12: Find the multiplicative inverse of the complex number .
- Q13: Find the multiplicative inverse of the complex number $-i$.
- Q14: Express the following expression in the form of $a + ib$:
CBSE Solutions for Class 11 Mathematics Complex Numbers
Chapters in CBSE - Class 11 Mathematics
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