Find the multiplicative inverse of the following complex numbers:… - Vidyadip

Question

Find the multiplicative inverse of the following complex numbers:
$1-\text{i}$

✓

Answer

If $\text{z}=\text{x}+\text{iy}$ is a complex number, then the multiplicative inverse of z, denoted by $\text{z}^{-1}$ or $\frac{1}{\text{z}}$ is defined as $\text{z}^{-1}=\frac{1}{\text{z}}$
$=\frac{1}{\text{x}+\text{iy}}$
$=\frac{1}{\text{x}+\text{iy}}\times\frac{\text{x}-\text{iy}}{\text{x}-\text{iy}}$
$=\frac{\text{x}-\text{iy}}{\text{x}^2+\text{y}^2}$
$=\frac{\text{x}}{\text{x}^2+\text{y}^2}-\frac{\text{y}}{\text{x}^2+\text{y}^2}\text{i}$
Given
$\text{z}=1-\text{i}$
$\therefore \ \text{z}^{-1}=\frac{1}{1^2+1^2}-\frac{(-1)}{1^2+1^2}\times\text{i}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Complex Numbers→Complex Numbers — all question types→Maths STD 11 Science question papers→CBSE Board STD 11 Science question papers→CBSE Board question paper generator→

Similar questions

A man saves ₹ 32 during the first year, ₹ 36 in the second year and in this way he increases his savings by ₹ 4 every year. Find in what time his saving will be ₹ 200.

Reduce the following equations to the normal form and find p and $\alpha$ in each case:
$\text{x}-3=0$

$(\text{c}^2-\text{a}^2+\text{b}^2)\tan\text{A}=(\text{a}^2-\text{b}^2+\text{c}^2)\tan\text{B}=(\text{b}^2-\text{c}^2+\text{a}^2)\tan\text{C}$

Find the equation of the circle which circumscribes the triangle formed by the lines
$x + y + 3 = 0, x - y + 1 = 0$ and $x = 3$

Let A = {1, 2, 3, 4} and $\text{R}=\{(\text{a},\text{b}):\text{a}\in\text{A},\text{b}\in\text{A},\text{ a divides b}\}.$ Write R explicitly.

From a well shuffled deck of 52 cards, 4 cards are drawn at random. What is the probability that all the drawn cards are of the same colour.

Find the ratio in which the line joining (2, 4, 5) and (3, 5, 4) is divided by the yz-plane.

Solve the following linear inequations in R:
$\text{x}-2\leq\frac{5\text{x}+8}{3}$

If a, b, c are in G.P., prove that:
$\frac{(\text{a}+\text{b}+\text{c})^2}{\text{a}^2+\text{b}^2+\text{c}^2}=\frac{\text{a}+\text{b}+\text{c}}{\text{a}-\text{b}+\text{c}}$

Show that the points $(3, -2), (1, 0), (-1, -2)$ and $(1, -4)$ are concyclic.