What is |3(2+i)-4(3-2i)| ?

The solution to |3(2+i)-4(3-2i)| is square root of 157

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simplify |3(2+i)-4(3-2i)|

simplify

∣ 3 (2 + i) - 4 (3 - 2 i) ∣

157

Decimal Notation

12.52996 \dots

Solution steps

∣ 3 (2 + i) - 4 (3 - 2 i) ∣

Expand

3 (2 + i) - 4 (3 - 2 i) : 11 i - 6

= ∣ 11 i - 6 ∣

Rewrite

11 i - 6

in standard complex form:

- 6 + 11 i

= ∣ - 6 + 11 i ∣

Apply complex arithmetic rule:

∣ a + bi ∣ = a^{2} + b^{2}

∣ - 6 + 11 i ∣ = (- 6)^{2} + 1 1^{2}

= (- 6)^{2} + 1 1^{2}

1 1^{2} = 121

= (- 6)^{2} + 121

(- 6)^{2} + 121 = 157

= 157

18 - 32

- \frac{8}{5} - 2

6 x^{2} + 2 x - 8

n^{2} - 2 n - 3

50 r^{2} - 72

What is |3(2+i)-4(3-2i)| ?
The solution to |3(2+i)-4(3-2i)| is square root of 157