2x^4+5x^3+7x^2-x+41, when x=-2-3i - Vidyadip

Question

$2\text{x}^4+5\text{x}^3+7\text{x}^2-\text{x}+41,$ when $\text{x}=-2-\sqrt{3}\text{i}$

✓

Answer

$\text{x}=-2-\sqrt{3}\text{i}$ $\text{x}^2=(-2-\sqrt{3}\text{i})^2=4+4\sqrt{3}\text{i}+3\text{i}^2=1+4\sqrt{3}\text{i}$ $\text{x}^3=(1+4\sqrt{3}\text{i})(-2-\sqrt{3}\text{i})=-2-8\sqrt{3}\text{i}-\sqrt{3}\text{i}-12\text{i}^2=10+9\sqrt{3}\text{i}$ $\text{x}^4=(1-4\sqrt{3}\text{i})^2=1+8\sqrt{3}\text{i}+48\text{i}^2=-47+8\sqrt{3}\text{i}$ $2\text{x}^4+5\text{x}^3+7\text{x}^2-\text{x}+41$ $=2(-47)+8\sqrt{3}\text{i})+5(10-9\sqrt{3}\text{i})+7(1+4\sqrt{3}\text{i})-(-2-\sqrt{3}\text{i})+41$ $=-94+16\sqrt{3}\text{i}+50-45\sqrt{3}\text{i}+7+28\sqrt{3}\text{i}+2+\sqrt{3}\text{i}+41$ $=(-94+50+7+2+41)+(16\sqrt{3}\text{i}-45\sqrt{3}\text{i}+28\sqrt{3}\text{i}+\sqrt{3}\text{i})$ $=6+0$ $=6$

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 4 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

Calculate the standard deviation for the following data:

Class:	0-30	30-60	60-90	90-120	120-150	150-180	180-210
Frequency:	9	17	43	82	81	44	24

Find the distance of the line 2x + y = 3 from the point (-1, -3) in the direction of the line whose slope is 1.

Solve the following equations: $\cot\text{x}+\tan\text{x}=2$

Find the sum of all two digit numbers which when divided by 4, yields 1 as remainder.

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{{\pi}}}\frac{\sqrt{2+\cos\text{x}-1}}{(\pi-\text{x})^2}$

Evaluate the following limit: $\lim\limits_{\text{x}\rightarrow{\text{a}}}\frac{\text{x}^{\frac{5}{7}}-\text{a}^{\frac{5}{7}}}{\text{x}^{\frac{2}{7}}-\text{a}^{\frac{2}{7}}}$

Show that the origin is equidistant from the lines $4x + 3y + 10 = 0; 5x - 12y + 26 = 0$ and $7x + 24y = 50$.

Find the sum of the following series up to n terms: $\frac { 1 ^ { 3 } } { 1 } + \frac { 1 ^ { 3 } + 2 ^ { 3 } } { 1 + 3 } + \frac { 1 ^ { 3 } + 2 ^ { 3 } + 3 ^ { 3 } } { 1 + 3 + 5 } + \ldots \ldots$

If $\alpha$ and $\beta$ are different complex numbers with $|\beta|=1,$ then find $\Big|\frac{\beta-\alpha}{1-\bar{\alpha}\beta}\Big|.$

Find the general solution for each of the following equations: $\sin\text{x}+\sin3\text{x}+\sin5\text{x}=0$