Question

If the modulus is 4 and the real part is 2.0, what is the imaginary part?

Answer 1

ANSWER

$2 \sqrt{3} i$

EXPLANATION

We we're given that, the real part of the complex number is 2.

Let the imaginary part be y.

Then the complex number is

$z = 2 + yi$

Also, we have that, the modulus is 4.

The modulus is given by the formula;

$|z| = \sqrt{ {x}^{2} + {y}^{2} }$

This implies that,

$4 = \sqrt{ {2}^{2} + {y}^{2} }$

We square both sides to obtain;

${4}^{2} = 4 + {y}^{2}$

$16 - 4 = {y}^{2}$

${y}^{2} = 12$

$y = \sqrt{12} = 2 \sqrt{3}$

Therefore the complex part is

$2 \sqrt{3} i$

Answer 2

Answer:

3.4

Step-by-step explanation:

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