MyQuestionIcon

1

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

Complex Numbers

Perform the i...

Question

Perform the indicated operations.
$(- 1 + \sqrt{3 i})^{3} .$

Open in App

Solution

$(a + b)^{3} = a^{3} + b^{3} + 3 a^{2} b + 3 a b^{2}$
$(- 1 + \sqrt{3 i})^{3} = (- 1)^{3} + (\sqrt{3 i}) + (\sqrt{3 i}) + (\sqrt{3 i}) + 3 (- 1)^{2} (\sqrt{3 i}) + 3 (- 1) (\sqrt{3 i})^{2}$
$= - 1 + 3 i \sqrt{3 i} + 3 \sqrt{3 i} - 3 \times 3 i$
$= - 1 + 3 i \sqrt{3 i} + 3 \sqrt{3 i} - 9 i$

Suggest Corrections

thumbs-up

0

Similar questions

Q. Perform the indicated operations:

(5 + 3 i) (3 - 2 i)

Q. Perform the indicated operations:

\frac{(+ 12 \times - 2)}{(- 4)} =

Q. Perform the indicated operations.

(1 + i)^{20} .

Q. Perform the indicated operations.

(1 + c o s ϕ + i s i n ϕ)^{n} .

Q. Perform the indicated operations:

(3) (2) (1) (0) (- 1) (- 2) (- 3) =

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