The value of (1+i)^4+(1-i)^4 is : - Vidyadip

MCQ

The value of $(1+\text{i})^4+(1-\text{i})^4$ is :

A
$8$
B
$4$
✓
$-8$
D
$-4$

✓

Answer

Correct option: C.

$-8$

Using $\text{a}^4+\text{b}^4=(\text{a}^2+\text{b}^2)^2-2\text{a}^2\text{b}^2$
$(1+\text{i})^4+(1-\text{i})^4$
$=\Big((1+\text{i})^2+(1-\text{i})^2\Big)^2-2(1+\text{i})^2(1-\text{i})^2$
$=(1+\text{i}^2+2\text{i}+1+\text{i}^2-2\text{i})^2-2(1+\text{i}^2+2\text{i})(1+\text{i}^2-2\text{i})$
$=(1-1+2\text{i}+1-1-2\text{i})^2-2(1-1+2\text{i})(1-1-2\text{i})$
$=(0)-2(2\text{i})(-2\text{i}) \ (\because\text{i}^2=-1)$
$=8\text{i}^2$
$=-8$

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 "MCQ" from Complex Numbers→Complex Numbers — all question types→Maths STD 11 Science question papers→Maharashtra Board STD 11 Science question papers→Maharashtra Board question paper generator→

Similar questions

$\sum_{r=1}^n(2 r-1)=x, \text { then }$
$\lim _{n \rightarrow \infty}\left[\frac{1^3}{x^2}+\frac{2^3}{x^2}+\frac{3^3}{x^2}+\ldots+\frac{n^3}{x^2}\right]=$

The mean of 5 observations is 4.4 and variance is 8.24. If three of the five observations are 1,2 and 6 , then the values of other two observations are

$\tan100^{\circ}+\tan125^{\circ}+\tan100^{\circ}\tan125^{\circ}=$

Number of all four digit numbers having different digits formed of the digits $\{1, 2, 3, 4\}$ and $5$ and divisible by $4$ is :

Equation of the straight line making equal intercepts on the axes and passing through the point (2, 4) is

If the domain of function $f ( x )=x^2-6 x+7$ is $(-\infty, \infty)$, then the range of function is

The intercept of a line between the coordinate axes is divided by the point (-5, 4) in the ratio 1: 2 . The equation of the line will be

If $\sin \theta=3 \sin (\theta+2 \alpha)$, then the value $\tan (\theta+\alpha)+2 \tan \alpha$ is

$\big(\sqrt{-2}\big)\big(\sqrt{-3}\big)$ is equal to :

If the lines 2x + 3y + 1 = 0 and 3x -y - 4 = 0 lie along diameters of a circle of circumferenc $10 \pi$ , then the equation of the circle is