## Related questions with answers

Question

Write the given number in the form $a+i b$. $i(1-i)(2-i)(2+6 i)$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2Use the scalar multiplication and multiplication properties of complex numbers in order to simplify the expression.

$\begin{align*} i\left(1-i\right)\left(2-i\right)\left(2+6i\right)&=\left(i-i^2\right)\left(2-i\right)\left(2+6i\right)\\ &=\left[i-\left(-1\right)\right]\left(4+12i-2i-6i^2\right)\\ &=\left(1+i\right)\left[4+10i-6\left(-1\right)\right]\\ &=\left(1+i\right)\left(10+10i\right)\\ &=10+10i+10i+10i^2\\ &=10+20i+10\left(-1\right)\\ &=0+20i\\ &=20i \end{align*}$

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