What is (1-3i)(1-i)(1+i)(1+3i) ?

The solution to (1-3i)(1-i)(1+i)(1+3i) is 20

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simplify (1-3i)(1-i)(1+i)(1+3i)

simplify

(1 - 3 i) (1 - i) (1 + i) (1 + 3 i)

20

Solution steps

(1 - 3 i) (1 - i) (1 + i) (1 + 3 i)

Apply complex arithmetic rule:

(a + bi) (a - bi) = a^{2} + b^{2}

= (1^{2} + (- 3)^{2}) (1 - i) (1 + i)

Apply complex arithmetic rule:

(a + bi) (a - bi) = a^{2} + b^{2}

= (1^{2} + (- 3)^{2}) (1^{2} + (- 1)^{2})

(1^{2} + (- 3)^{2}) (1^{2} + (- 1)^{2}) = 20

= 20

\frac{( x ^{4} \cdot y ^{- 2} ) ^{- 3}}{( 2 x ^{- 3} \cdot y ^{2} ) ^{2}}

\frac{4}{3 x} - \frac{5}{7}

\frac{6 x ^{2} + x - 2}{9 x ^{2} - 4}

(z - 4)^{2}

4 x (3 x - 7) - 19 x^{2}