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

Question

Express the following complex numbers in the standard form a + ib: $\frac{3+2\text{i}}{-2+\text{i}}$

✓

Answer

$\frac{3+2\text{i}}{-2+\text{i}}=\frac{3+2\text{i}}{(-2+\text{i})}\times\frac{(-2-\text{i})}{-2-\text{i}}$ [Rationalising the denominator] $=\frac{3(-2-\text{i})+2\text{i}(-2-\text{i})}{(-2)^2-(\text{i}^2)} \ \big[\because \ (\text{a}+\text{ib})(\text{a}-\text{ib})=\text{a}^2+\text{b}^2\big]$ $=\frac{-6-3\text{i}-4\text{i}+2}{4+1} \ \big[\because \ -\text{i}^2=1\big]$ $=\frac{-4-7\text{i}}{5}$ $=\frac{-4}{5}-\frac{7}{5}\text{i}$ $\therefore \ \frac{3+2\text{i}}{-2+\text{i}}=\frac{-4}{5}-\frac{7}{5}\text{i}$

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 "(Each question 1 marks)" from Complex Numbers→Complex Numbers — all question types→MATHS STD 11 Science question papers→Gujarat Board STD 11 Science question papers→Gujarat Board question paper generator→

Similar questions

On her vacations Veena visits four cities (A, B, C and D) in a random order. What is the probability of A before B?

If $\frac{(\text{a}^2+1)^2}{2\text{a}-\text{i}}=\text{x}+\text{iy},$ find the value of $\text{x}^2+\text{y}^2.$

Write the negation of the following statements: All triangles are not equilateral triangle.

Check whether the probabilities P(A) and P(B) are consistently defined P(A) = 0.5. P(B) = 0.7, $P(A \cap B) $ = 0.6

Make correct statementby fillingthe symbol$\subset$or$\not\subset$in the blank space:{x: x is a triangle in a plane}......... {x : x is a rectangle in the same plane}

Write the following statements in the form "if p, then q". It rains only if it is cold.

If A = {(x, y): y = $\frac{1}{\text{x}},$ 0 $\not=$ x $\in$ R} and B = {(x, y) = -x, x $\in$ R}, then write $\text{A}\cap\text{B.}$

Write the following statements in the form "if p, then q". The game is cancelled only if it is raining.

Let a sample space be S = {$\omega_1, \omega_2,..., \omega_6$}.Which of the following assignments of probabilities to each outcome are valid?

Outcomes	$\omega_1$	$\omega_2$	$\omega_3$	$\omega_4$	$\omega_5$	$\omega_6$
	$\frac 16$	$\frac 16$	$\frac 16$	$\frac 16$	$\frac 16$	$\frac 16$

If a and b are roots of the equation $x^2− px + q = 0$, than write the value of $\frac{1}{\text{a}}+\frac{1}{\text{b}}.$