Express the following complex numbers in the standard form a + ib… - Vidyadip

Question

Express the following complex numbers in the standard form a + ib:
$\frac{5+\sqrt{2}\text{i}}{1-\sqrt{2}\text{i}}$

✓

Answer

We have,
$\frac{5+\sqrt{2}\text{i}}{1-\sqrt{2}\text{i}}=\frac{5+\sqrt{2}\text{i}}{1-\sqrt{2}\text{i}}\times\frac{1+\sqrt{2}\text{i}}{1+\sqrt{2}\text{i}}$
$=\frac{5(1+\sqrt{2}\text{i})+\sqrt{2}\text{i}(1+\sqrt{2}\text{i})}{1+2}$
$=\frac{5+5\sqrt{2}\text{i}+\sqrt{2}\text{i}-2}{3}$
$=\frac{3+6\sqrt{2}\text{i}}{3}$
$=1+2\sqrt{2}\text{i}$
$\therefore \ \frac{5+\sqrt{2}\text{i}}{1-\sqrt{2}\text{i}}=1+2\sqrt{2}\text{i}$

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 "2 Marks Questions" 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 die is thrown twice Each time the number appearing on it is recorded Describe the following events:
A = Both numbers are odd.

Find what the following equations become when the origin is shifted to the point $(1, 1)?$
$x^2 + y^2 − 2x − 2y = 0$

Evaluate the following limit:
$\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\text{logx}-\text{loga}}{\text{x}-\text{a}}$

If $x, y \in\{1,2,3\}$, then which of the relation are functions-
(i) $f_1=\{(x, y): x+y>3\}$
(ii) $f_2=\{(x, y): x>3\}$
(iii) $f_3=\{(x, y): y=x+1\}$
(iv) $f_4=\{(x, y): x+y=4\}$

In an examination$,$ a student has to answer $4$ questions out of $5$ questions; questions $1$ and $2$ are however compulsory. Determine the number of ways in which the student can make the choice.

For what values of x, the numbers $ \frac { - 2 } { 7 } , x , \frac { - 7 } { 2 }$ are in G.P.?

A bag contains 2 red and white balls. three balls are drawn at random. find the probability that:
One ball is red and two balls are white.

If A = {1, 2, 3, 4, 5}, B = {4, 5, 6, 7, 8}, C = {7, 8, 9, 10, 11}, and D = {10, 11, 12, 13, 14}. Find:
$\text{A}\cup\text{B}\cup\text{C}$

If $R_3= (x, |x| ) |x$ is a real number is a relation. Then find domain and range of $R_3.$

Find the 12th term from the end of the following arithmetic progressions,

1, 4, 7, 10, ..., 88