How do you simplify |2+3i|?

Answered question

2022-01-17

How do you simplify |2+3i|?

Answer & Explanation

nick1337

nick1337

Expert2022-01-18Added 777 answers

Step 1 Given: |2+3i| |a+bi|=a2+b2 So, |2+3i|=22+32 4+9 13 Hence, |2+3i|=13
Vasquez

Vasquez

Expert2022-01-18Added 669 answers

Step 1 The inverse of 2+3i is 12+3i In general case, multiply the expression 1a+bi by the conjugate (the conjugate of a+ib is aib): 1a+ib=1(aib)(a+ib)(aib) Expand the denominator: 1(aib)(a+ib)(aib)=aiba2+b2 Split: aiba2+b2=aa2+b2iba2+b2 In our case, a=2 and b=3 Therefore, (12+3i)=(2133i13) Hence, 12+3i=2133i13
alenahelenash

alenahelenash

Expert2022-01-24Added 556 answers

Step 1 We have that a=2 and b=3 Thus, r=(2)2+(3)2=13 Also, θ=atan(32)=atan(32) Therefore, 2+3i=13(cos(atan(32))+isin(atan(32)))

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