Question

find the value of (3+2/i)(i^6-i^7)(1+i^11)

Answer 1

the value is
=2(2+3i)

Answer 2

Answer:

6i+4

Step-by-step explanation:

The given expression is $(3+\frac{2}{i}))i^6-i^7)(1+i^{11})$

We can rewrite this expression as

$(3+\frac{2}{i})((i^2)^3-(i^2)^3i(1+(i^2)^5i)$

We know that $i^2=-1$

Thus, the expression becomes

$(3+\frac{2}{i})((-1)^3-(-1)^3i(1+(-1)^5i)\\\\=(3+\frac{2}{i})(-1+i)(1-i)$

Now. rationalize the denominator by multiplying numerator and denominator by i

$(3+\frac{2}{i}\cdot\frac{i}{i})(-1+i)(1-i)\\\\=(3+\frac{2i}{i^2}(-1+i)(1-i)\\\\=(2i-3)(1-i)(1-i)\\\\=(2i-3)(1+i^2-2i)\\\\=(2i-3)(1-1-2i)\\\\=2i(3-2i)\\\\=6i-4i^2\\\\=6i+4$

Therefore, the simplified form is 6i+4