alleryThe value of $i^3$ is:
- $i$
- $-1$
- $-i$
- $1$
Show answer and solution
Correct answer: C. $-i$
We have i³ = i²·i.
That is i³ = (−1)i.
So i³ = −i.
JEE Main Unit 3A: Chain Rule and Composite Functions — practice questions
Explore 12 free Unit 3A: Chain Rule and Composite Functions questions in JEE Main Mathematics. Open each question or exercise to read its content, reference answers and available explanation.
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Showing questions 1–12 of 12.
The value of $i^3$ is:Read the answer and worked solution →For the complex number $z = 2 + 5i$, the imaginary part $\operatorname{Im}(z)$ is:Read the answer and worked solution →The complex conjugate of $3 - 4i$ is:Read the answer and worked solution →The modulus $|3 + 4i|$ equals:Read the answer and worked solution →The multiplicative inverse of $i$ (i.e. $1/i$) is:Read the answer and worked solution →The value of $i^{10}$ is:Read the answer and worked solution →The value of $(1 + i)^2$ is:Read the answer and worked solution →The roots of the equation $x^2 + 1 = 0$ are:Read the answer and worked solution →The modulus $|1 - i|$ equals:Read the answer and worked solution →The product $(2 + 3i)(2 - 3i)$ equals:Read the answer and worked solution →The value of $i + i^2 + i^3 + i^4$ is:Read the answer and worked solution →If $z = a + ib$ is non-zero, its multiplicative inverse $z^{-1}$ is:Read the answer and worked solution →
Worked practice questions
For the complex number $z = 2 + 5i$, the imaginary part $\operatorname{Im}(z)$ is:
- 5
- $5i$
- $-5$
- 2
Show answer and solution
Correct answer: A. 5
For z = a + ib, the imaginary part is b; here Im(z) = 5.
The complex conjugate of $3 - 4i$ is:
- $-3 - 4i$
- $4 - 3i$
- $3 + 4i$
- $-3 + 4i$
Show answer and solution
Correct answer: C. $3 + 4i$
The conjugate of a + ib is a − ib, so conj(3 − 4i) = 3 + 4i.
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