(C) Given $z = 1 + i$ and $i = \sqrt{-1}$.Squaring both sides,we get $z^2 = (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i$.The multiplicative inverse of

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) Given $z = 1 + i$ and $i = \sqrt{-1}$.Squaring both sides,we get $z^2 = (1 + i)^2 = 1 + 2i + i^2 = 1 + 2i - 1 = 2i$.The multiplicative inverse of $z^2$ is $\frac{1}{z^2} = \frac{1}{2i}$.To simplify,multiply the numerator and denominator by $i$:$\frac{1}{2i} \times \frac{i}{i} = \frac{i}{2i^2} = \frac{i}{2(-1)} = -\frac{i}{2}$.

Class 11 Mathematics 4-1.Complex numbers Integral power of iota, Algebraic operations and Equality of complex numbers

Easy

If $z = 1 + i,$ then the multiplicative inverse of $z^2$ is (where $i = \sqrt{-1}$)

A
$2i$
B
$1 - i$
C
$-i/2$
D
$i/2$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

4-1.Complex numbers

Subtopic

Integral power of iota, Algebraic operations and Equality of complex numbers

Let $x$ and $y$ be real numbers such that $50 \left(\frac{2x}{1 + 3i} - \frac{y}{1 - 2i}\right) = 31 + 17i$, where $i = \sqrt{-1}$. Then the value of $10(x - 3y)$ is:

DifficultJEE MAIN 2026

View Solution

The imaginary part of $\frac{(1-i)^3}{(2-i)(3-2i)}$ is

EasyAP EAMCET 2024

View Solution

If $\left(\frac{1-i}{1+i}\right)^{96}=a+ib$,then $(a, b)$ is

MediumKCET 2018

View Solution

If ${i^2} = -1$,then the sum $i + {i^2} + {i^3} + \dots$ up to $1000$ terms is equal to

Easy

View Solution

Express the given complex number in the form $a+ib$: $\left(-2-\frac{1}{3}i\right)^{3}$

Medium

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $z = 1 + i,$ then the multiplicative inverse of $z^2$ is (where $i = \sqrt{-1}$)

Similar Questions

Let $x$ and $y$ be real numbers such that $50 \left(\frac{2x}{1 + 3i} - \frac{y}{1 - 2i}\right) = 31 + 17i$, where $i = \sqrt{-1}$. Then the value of $10(x - 3y)$ is:

The imaginary part of $\frac{(1-i)^3}{(2-i)(3-2i)}$ is

If $\left(\frac{1-i}{1+i}\right)^{96}=a+ib$,then $(a, b)$ is

If ${i^2} = -1$,then the sum $i + {i^2} + {i^3} + \dots$ up to $1000$ terms is equal to

Express the given complex number in the form $a+ib$: $\left(-2-\frac{1}{3}i\right)^{3}$

Vedclass Test Series

Exam Paper Generator

Online Exam Module