Question

find the absolute value.
|-7 + 5i|
\sqrt{\boxed{?}}

Explanation:

Step1: Recall the formula for the absolute value of a complex number \( z = a + bi \), which is \( |z|=\sqrt{a^{2}+b^{2}} \).

For the complex number \( -7 + 5i \), we have \( a=-7 \) and \( b = 5 \).

Step2: Calculate \( a^{2}+b^{2} \).

Substitute \( a=-7 \) and \( b = 5 \) into the formula: \( (-7)^{2}+5^{2}=49 + 25 \).

Step3: Simplify the expression.

\( 49+25 = 74 \).

Answer:

74