How do you find the absolute value of the complex

Answered question

2022-01-17

How do you find the absolute value of the complex number z=34i?

Answer & Explanation

nick1337

nick1337

Expert2022-01-18Added 777 answers

Step 1 One way to do this is with the general formula |a+bi|=a2+b2 so that |34i|=32+(4)2=9+16=25=5 This formula is essentially the distance formula from the point (a, b) to the origin (0, 0) in the plane (in rectangular coordinates), which comes from the Pythagorean Theorem. Another way to show your work if z=a+bi is to write the answer as |z|=z×z¯ where z¯=abi is the complex conjugate of z. Since z×z¯=(a+bi)(abi)=a2abi+abib2i2=a2+b2 this gives the same answer.
Vasquez

Vasquez

Expert2022-01-18Added 669 answers

Step 1 Z=(3)2(4i)2 Z=9(16×1) Z=9+16 Z=25 Z=5
alenahelenash

alenahelenash

Expert2022-01-24Added 556 answers

Step 1 z=3+4i z¯=34i |z|=x2+y2 |z¯|=32+42 |z¯|=25=5

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