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Chapter 2: Problem 9

Find each product and write the result in standard form. $$-3 i(7 i-5)$$

Short Answer

Expert verified
The product, in standard form, is \(21 + 15i\).

Step by step solution

01

Distribute

Distribute the \( -3i \) across \( (7i-5) \) which gives \( -21i^2 + 15i \)
02

Use the identity \(i^2 = -1\)

Substitute \(i^2\) with \(-1\) in the expression obtained, which gives \(-21(-1) + 15i\). So the result becomes, \(21 + 15i\).
03

Write in standard form

The standard form of a complex number is \( a + bi \) where a and b are real numbers. Thus the standard form of the complex number is \(21 + 15i\)

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