What is i(4-i)+4i(1+2i) ?

The solution to i(4-i)+4i(1+2i) is -7+8i

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simplify i(4-i)+4i(1+2i)

simplify

i (4 - i) + 4 i (1 + 2 i)

- 7 + 8 i

Solution steps

i (4 - i) + 4 i (1 + 2 i)

Expand

i (4 - i) : 4 i + 1

= 4 i + 1 + 4 i (1 + 2 i)

Expand

4 i (1 + 2 i) : 4 i - 8

= 4 i + 1 + 4 i - 8

Group like terms

= 4 i + 4 i + 1 - 8

Add similar elements:

4 i + 4 i = 8 i

= 8 i + 1 - 8

Subtract the numbers:

1 - 8 = - 7

= 8 i - 7

Rewrite in standard complex form:

- 7 + 8 i

= - 7 + 8 i

1 \cdot 2^{- 2}

- 4 (- x + 2)^{2} + 2 (- x + 2) + 12

\frac{3}{4} + \frac{1}{20}

(1 - i) - i

(2 t + \frac{1}{t ^{2}})^{10}