Question

Áp dụng các hằng đẳng thức đáng nhớ để tính :

a) \(\left(2+i\sqrt{3}\right)^2\)

b) \(\left(1+2i\right)^3\)

c) \(\left(3-i\sqrt{2}\right)^3\)

d) \(\left(2-i\right)^3\)

Answer 1

a) ta có : \(\left(2+i\sqrt{3}\right)^2=2^2+2.2.i\sqrt{3}+\left(i\sqrt{3}\right)^2\)

\(=4+4\sqrt{3}i-3=1+4\sqrt{3}i\)

b) ta có : \(\left(1+2i\right)^3=1^3+3.1^2.2i+3.1.\left(2i\right)^2+\left(2i\right)^3\)

\(=1+6i-6-8i=-5-2i\)

c) \(\left(3-i\sqrt{2}\right)^3=3^3-3.3^2.i\sqrt{2}+3.3.\left(i\sqrt{2}\right)^2+\left(i\sqrt{2}\right)^3\)

\(=27-27\sqrt{2}i-18-2\sqrt{2}i=9-29\sqrt{2}i\)

d) \(\left(2-i\right)^3=2^3-2.2^2.i+2.2.i^2-i^3\)

\(=8-8i-4+i=4-7i\)