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Q1:
Express the complex number 
in the form $a + ib$.
Express the complex number in the form $a + ib$.
Solution :
Step 1: Given Expression and Objective
The objective is to express the complex number $z = 5i \times \left(-\frac{3}{5}i\right)$ in the standard form $a + ib$, where $a$ and $b$ are real numbers and $i = \sqrt{-1}$.
Step 2: Algebraic Manipulation and Distribution
Utilize the associative and commutative properties of complex multiplication [Per the Field Properties of Complex Numbers].
$z = 5 \times \left(-\frac{3}{5}\right) \times i \times i$
$z = -3 \times i^2$
Step 3: Application of the Imaginary Unit Property
By definition, the imaginary unit is defined as $i = \sqrt{-1}$, which implies the fundamental identity $i^2 = -1$ [By definition of the Complex Number System].
Substitute $i^2 = -1$ into the expression:
$z = -3 \times (-1)$
$z = 3$
Step 4: Mapping to Standard Form $a + ib$
To satisfy the requirement of the form $a + ib$, the real part $a$ is identified as $3$ and the imaginary part $b$ is identified as $0$.
$z = 3 + 0i$
Final Solution: 3 + 0i
More Questions from Class 11 Mathematics Complex Numbers EXERCISE 4.1
- 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 $a + ib$.
- Q6: Express the complex number 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
Top Tutors who teach Complex Numbers
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20 yrs of
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105 hrs of classes completed
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I am teacher with over experience of 20 years. Provides complete notes and assignment. And make subject more understanding and easy.
Took online one to one class , highly satisfy, sir is knowlegeble and experienced teacher and took regular test.
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I have been teaching students for the last 20 years. Many of my students had passed with more than 95% marks or higher grade. I always love interactive classes so always motivate my students to ask as many questions as they can.Once the teaching process becomes dialogue from monologue then I understand that half of the task has been done and thereafter concept building process becomes very easy as I constantly guided by the questions from my students. Keeping class regularly on time, solving questions everyday, clearing doubts on a regular basis and lastly keeping weekly test make it very simple to make a good score.
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I have approximately 3 years of experience of teaching Mathematics across different boards including CBSE, IGCSE and state board in reputed schools like DPS International. I am post graduate in statistics and honors degree in mathematics from reputed universities like DU. I have helped many students to overcome their fear of Mathematics and Statistics. My aim is to develop a genuine love for the subject in students.
You are a great teacher because of you, I love maths; otherwise, before I was counted among the maths haters.
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With years of experience teaching Class 11 Mathematics, I have honed my skills to provide students with a deep understanding of complex concepts. My teaching approach is student-centered, focusing on clarity, problem-solving techniques, and real-world applications. I have a strong command over the subject, making intricate topics accessible and engaging. My classes are interactive and designed to foster a genuine interest in mathematics. By incorporating innovative methods and advanced tools, I ensure that learning is both effective and enjoyable. Join my classes to experience a supportive learning environment where your academic success is the ultimate goal!
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