complex-number-multiplication

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Algorithms

A <a href="https://en.wikipedia.org/wiki/Complex_number" target="_blank">complex number</a> can be represented as a string on the form <code>&quot;real+imaginaryi&quot;</code> where:

<ul>
	<li><code>real</code> is the real part and is an integer in the range <code>[-100, 100]</code>.</li>
	<li><code>imaginary</code> is the imaginary part and is an integer in the range <code>[-100, 100]</code>.</li>
	<li><code>i2 == -1</code>.</li>
</ul>

Given two complex numbers <code>num1</code> and <code>num2</code> as strings, return a string of the complex number that represents their multiplications.

&nbsp;
Example 1:

<pre>
Input: num1 = &quot;1+1i&quot;, num2 = &quot;1+1i&quot;
Output: &quot;0+2i&quot;
Explanation: (1 + i) * (1 + i) = 1 + i2 + 2 * i = 2i, and you need convert it to the form of 0+2i.
</pre>

Example 2:

<pre>
Input: num1 = &quot;1+-1i&quot;, num2 = &quot;1+-1i&quot;
Output: &quot;0+-2i&quot;
Explanation: (1 - i) * (1 - i) = 1 + i2 - 2 * i = -2i, and you need convert it to the form of 0+-2i.
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>num1</code> and <code>num2</code> are valid complex numbers.</li>
</ul>

complexNumberMultiply

Complex Number Multiplication

Math

String

Simulation

<a href="https://baike.baidu.com/item/%E5%A4%8D%E6%95%B0/254365?fr=aladdin" target="_blank">复数</a> 可以用字符串表示，遵循 <code>"实部+虚部i"</code> 的形式，并满足下述条件：

<ul>
	<li><code>实部</code> 是一个整数，取值范围是 <code>[-100, 100]</code></li>
	<li><code>虚部</code> 也是一个整数，取值范围是 <code>[-100, 100]</code></li>
	<li><code>i2 == -1</code></li>
</ul>

给你两个字符串表示的复数 <code>num1</code> 和 <code>num2</code> ，请你遵循复数表示形式，返回表示它们乘积的字符串。

 

示例 1：

<pre>
输入：num1 = "1+1i", num2 = "1+1i"
输出："0+2i"
解释：(1 + i) * (1 + i) = 1 + i2 + 2 * i = 2i ，你需要将它转换为 0+2i 的形式。
</pre>

示例 2：

<pre>
输入：num1 = "1+-1i", num2 = "1+-1i"
输出："0+-2i"
解释：(1 - i) * (1 - i) = 1 + i2 - 2 * i = -2i ，你需要将它转换为 0+-2i 的形式。 
</pre>

 

提示：

<ul>
	<li><code>num1</code> 和 <code>num2</code> 都是有效的复数表示。</li>
</ul>