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MATH / The complex number z is equal to 9+bi, where b is a positive real number and i²=−1. Given that the imaginary parts of z² and z³ are equal, find b.

Problem

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problem

The complex number zz is equal to 9+bi9 + bi, where bb is a positive real number and i2=−1i^2 = -1. Given that the imaginary parts of z2z^2 and z3z^3 are equal, find bb.
Plain-text mathematical notation (without MathML)
The complex number z is equal to 9+bi, where b is a positive real number and i²=−1. Given that the imaginary parts of z² and z³ are equal, find b.
Original LaTeX notation
The complex number $z$ is equal to $9 + bi$, where $b$ is a positive real number and $i^2 = -1$. Given that the imaginary parts of $z^2$ and $z^3$ are equal, find $b$.

level

Level 3

type

Intermediate Algebra

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Source and history

task_id
05d8caeb-38a7-5564-a776-f2510b0703a1
task_key
intermediate~5falgebra--test--05d8caeb-38a7-5564-a776-f2510b0703a1
task_revision_id
1
config / split
intermediate_algebra / test

Official source

initial import