What is (isqrt(2)-1)(2isqrt(2)+3) ?

The solution to (isqrt(2)-1)(2isqrt(2)+3) is -7+sqrt(2)i

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simplify (isqrt(2)-1)(2isqrt(2)+3)

simplify

(i 2 - 1) (2 i 2 + 3)

- 7 + 2 i

Solution steps

(i 2 - 1) (2 i 2 + 3)

Rewrite

i 2 - 1

in standard complex form:

- 1 + 2 i

Rewrite

2 i 2 + 3

in standard complex form:

3 + 22 i

= (- 1 + 2 i) (3 + 22 i)

Apply complex arithmetic rule:

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

= (- 1 \cdot 3 - 2 \cdot 22) + (- 1 \cdot 22 + 2 \cdot 3) i

Simplify

(- 1 \cdot 3 - 2 \cdot 22) + (- 1 \cdot 22 + 2 \cdot 3) i : - 7 + 2 i

= - 7 + 2 i

∣ - 2 x ∣ = 4

\frac{x ^{2}}{x ^{- 2}}

5 x - 12 = 2 x + 24

\frac{1}{8} + c = \frac{4}{5}

(- 2 x^{5} y^{7})^{3} + 7 x^{15} y^{21}

What is (isqrt(2)-1)(2isqrt(2)+3) ?
The solution to (isqrt(2)-1)(2isqrt(2)+3) is -7+sqrt(2)i