$\sqrt{\text{Imaginary}}$

Algebra Level 3

$\large (\sqrt i)^6 \times (\sqrt i)^{16} = ?$

1+i

i

1

0

2 + i

-1

-i

1 solution

Chew-Seong Cheong
Oct 29, 2017

$\begin{aligned} \left(\sqrt i\right)^6\left(\sqrt i\right)^{16} & = \left(i^\frac 12 \right)^6\left(i^\frac 12 \right)^{16} = i^3i^8 = i^{11} = \left(i^2\right)^5i = (-1)^5i = \boxed{-i} \end{aligned}$

How $i^{4+4+3} = i^3$ ?

Nazmus sakib - 3 years, 7 months ago

$i^4=(i^2)^2 = (-1)^2 = 1$

Chew-Seong Cheong - 3 years, 7 months ago

Imaginary \sqrt{\text{Imaginary}} Imaginary ​

1 solution

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$\sqrt{\text{Imaginary}}$