What is (-1+i)(1/(sqrt(2))+1/(sqrt(2))i) ?

The solution to (-1+i)(1/(sqrt(2))+1/(sqrt(2))i) is -1/(sqrt(2))-1/(sqrt(2))

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simplify (-1+i)(1/(sqrt(2))+1/(sqrt(2))i)

simplify

(- 1 + i) (\frac{1}{2} + \frac{1}{2} i)

- \frac{1}{2} - \frac{1}{2}

Decimal Notation

- 1.41421 \dots

Solution steps

(- 1 + i) (\frac{1}{2} + \frac{1}{2} i)

Apply complex arithmetic rule:

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i

= (- 1 \cdot \frac{1}{2} - 1 \cdot \frac{1}{2}) + (- 1 \cdot \frac{1}{2} + 1 \cdot \frac{1}{2}) i

Simplify

(- 1 \cdot \frac{1}{2} - 1 \cdot \frac{1}{2}) + (- 1 \cdot \frac{1}{2} + 1 \cdot \frac{1}{2}) i : - \frac{1}{2} - \frac{1}{2}

= - \frac{1}{2} - \frac{1}{2}

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What is (-1+i)(1/(sqrt(2))+1/(sqrt(2))i) ?
The solution to (-1+i)(1/(sqrt(2))+1/(sqrt(2))i) is -1/(sqrt(2))-1/(sqrt(2))