How to simplify this imaginary expression?

Question

#(-6i^4)(2i^3)(-3i^4)#

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Answer 1 · 2017-08-19T00:00:57

#-36i#

We're asked to simplify

#-6i^4 * 2i^3 * -3i^4#

Let's multiply through the coefficients, and then multiply the complex numbers:

#= 36i^(4+3+4)#

#= 36i^11#

Remember that #i^2 = -1#, so we have

#= 36(i^2)(i^2)(i^2)(i^2)(i^2)i#

#= 36(-1)(-1)(-1)(-1)(-1)i#

#= color(blue)(ulbar(|stackrel(" ")(" "-36i" ")|)#