Question

Express the following in the form a + bi, where a and b are real numbers:
$\sqrt{60i - 11}$
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Answer 1

The equivalent of the complex number expression is $\sqrt{60i - 11}$ is 2 + 15i

How to rewrite the expression?

The complex number expression is given as:

$\sqrt{60i - 11}$

Rewrite as:

$a + bi = \sqrt{60i - 11}$

Take the square of both sides

$a^2 + 2abi - b = 60i - 11$

By comparison, we have:

a^2 - b = -11

2ab = 60

Divide both sides by 2

ab = 30

Using a graphical tool, we have:

a = 2,b = 15

So, we have:

a + bi = 2 + 15i

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