MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Complex Numbers

Find the valu...

Question

Find the value of $x^{3} + 2 x^{2} - 3 x + 21$ if $x = 1 + 2 i$

Open in App

Solution

$x^{3} + 2 x^{2} - 3 x + 21$ if $x = 1 + 2 i$
$(x - 1)^{2} = (2 i)^{2}$
$x^{2} - 2 x + 1 = - 4$
$x^{2} - 2 x + 5 = 0$
$∴ x^{3} + 2 x^{2} - 3 x + 21$
$= x (x^{2} - 2 x + 5) + 4 x^{2} - 8 x + 21$
$= 0 + 4 x^{2} - 8 x + 21$
$= 4 (x^{2} - 2 x + 5) + 1$
$= 0 + 1$
$= 1$
Value is $1$ .

Suggest Corrections

thumbs-up

0

Similar questions

Q. Find the value of

x^{3} + 7 x^{2} - x + 16

x = 1 + 2 i

x = 1 + \sqrt{2}

then find the value of the expression

x^{4} - x^{3} - 2 x^{2} - 3 x + 1

x = 1 + 2^{1 / 3} + 2^{2 / 3}

then find the value of

x^{3} - 3 x^{2} - 3 x - 1

f (x) = 2 x^{2} - x + 1

g (x) = x^{3} - 3 x + 1

, then the value of

f (1) + g (- 1)

x = 1 + 2 i

, then find the value of

x^{3} + x^{2} - x + 22 w h e r e i = \sqrt{- 1}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Introduction

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Complex Numbers

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon