mod(3+4i) — step-by-step solution

The complex number

a + i b

has modulus

\sqrt{a^{2} + b^{2}}

, so:

ⅰ

\mod (3 + 4 i)

\sqrt{3^{2} + 4^{2}}

\sqrt{3^{2} + 4^{2}}

ⓘ Powers are computed before multiplications, additions and subtractions. With a positive integer exponent, a power corresponds to a repeated product:

3^{2}

3 \times 3

9

4^{2}

4 \times 4

16

\sqrt{9 + 16}

ⓘ Start by calculating what is inside the parentheses:

9 + 16

25

\sqrt{25}

ⓘ The square root of a nonnegative real number is the nonnegative number whose square is that number:

\sqrt{25}

5

because

5^{2}

25

▶Result:

5