Question

conjugate of (5+✓2i)^2​

Answer 1

Answer:

(5-root2)^2

Step-by-step explanation:

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Answer 2

Answer:

Step-by-step explanation:

Concept:

Mathematicians who work with complex numbers sometimes see conjugate pairs of complex roots. Therefore, the middle of the binomial terms will have an opposite sign (roots). Mathematical conjugates are remarkably good at making sense of complex numbers and radical expressions.

When the sum and product of the binomial and its conjugate are rational, the conjugate is created by switching the sign between two terms in the binomial. The binomial in this case can either be a simple or complex number.

Given:

$(5+\sqrt{2i} )^{2}$

Find:

To find the conjugate of $(5+\sqrt{2i} )^{2}$

Solution:

Given $(5+\sqrt{2i} )^{2}$

By using the $(a+b)^{2} = a^{2} + 2ab+ b^{2}$ then we will get

$(5^{2} + 2 * 5 * \sqrt{2i} + \sqrt{2i} ^{2} )$

$25-2i + 10\sqrt{2i}$

$23 + 10\sqrt{2i}$

$23-10\sqrt{2i}$

Hence the conjugate of $(5+\sqrt{2i})^{2}$ is $23-10\sqrt{2i}$

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