Question

express in a+ib form (1+2i)^6 (4i+3)^3​

Answer 1

Answer:

$(1+2i)^6(4i+3)^3=-3125$

Step-by-step explanation:

Express in a+ib form (1+2i)^6 (4i+3)^3​

$(1+2i)^6(4i+3)^3$

$=[(1+2i)^2]^3(4i+3)^3$

using

$\boxed{(a+b)^2=a^2+b^2+2ab}$

$=[1+4i^2+4i]^3(4i+3)^3$

$=[1-4+4i]^3(3+4i)^3$

$=(-3+4i)^3(3+4i)^3$

$=-(3-4i)^3(3+4i)^3$

$=-[(3-4i)(3+4i)]^3$

using

$\boxed{(a-b)(a+b)=a^2-b^2}$

$=-[3^2-4^2i^2]^3$

$=-[9+16]^3$

$=-(25)^3$

$=-3125$

$\implies\boxed{(1+2i)^6(4i+3)^3=-3125}$